b2 + 5 = 8b 10 b. 9 1 = 9 3x2 14x + 8 The coefficient is \(\sqrt{7}\). -7 = -2x + y Answer: Question 24. = (4x 3)(x + 2x + x + 2) LHS = RHS (x 1)(2x 5), Question 4. (s + 5)(s 5) = s 5 3 (2x2 4x+ 7) b. (x + 22)(x 15) = 0 w(w 8w + 16) = 0 w = 0, 6. Answer: Factored Form Standard Form Nonstandard Form Identify the degree and leading coefficient of the polynomial. Name: Date: Directions: Factor each polynomia 1. x2 + 5x + 6 3. m2 + 18m + 56 5. y2 + 9y + 8 7. y2 - 6y + 8 9. n - n - 90 11. x2 + 3x - 70 13. m2 + 5m - 6 15. x2 - 10x - 39 17. x2 . Edit your all things algebra answer key unit 7 online Type text, add images, blackout confidential details, add comments, highlights and more. Answer: x + 16 + 11x + 176 Answer: Question 26. Answer: -x + 3x 2x + 6 Write a binomial that represents the height of the projection. (z + 11)(z 11) -r 10 + 4r r 7r (4x + 3) + (x 2) Doing so is a violation of copyright. Check your solution. 8y2 24y = 8y(y 3) An exponential function j models a relationship in which the dependent variable is multiplied by 6 for every 1 unit the independent variable increases. The Parthenon in Athens, Greece, is an ancient structure that has a rectangular base. Fluency skills are emphasized throughout the unit. WHICH ONE DOESNT BELONG? x = -5 Then identify the degree of the sum or difference and classify it by the number of terms. = 30 8 Lesson #10 - Translating English to Algebra Lesson #11 - Algebraic Puzzles . Answer: Question 4. = -11d(2d 1) + 9(2d 1) x 72 = 0 or x + 72 = 0 = (m + 12), Question 22. 4y 7y + 28 = 16y A = 624 sq. Combine the like terms = 4x + 120x + 3456, c. Find the perimeter and the area of the blanket including the fringe when the width of the fringe is 4 inches. = (h + 2)(-8h + 3), Question 22. What is the value of x? a. V = lbh -3x2 x + 2 n. x + 4x + 4x = x(x + 4x + 4) = x(x + 2) H x(x 11) -2(x 11) b = -d = -5t t + 8t + 3 4 (-5g 2h)(-5g + 2h) l = 2w + 4 Algebra Expressions With Tiles . 39x 17x 376 = 0 Please dont put the software, your login information or any of our materials on a network where people other than you can access it. Question 19. (x + 7) = x + 7 + 2(x)(7) Answer: 4x2 = 2x a. x3 + 4x2 + 3x A polynomial that models the possible gene combinations of the offspring is Answer: Answer: At the same time, your friend throws a ball upward. (x 1)(x 1)(x 2)(x 3) = 0. z2 + 10z + 21 Unit 7: Polynomials & Factoring Review 1 Name Play this game to review Algebra I. w3 8w2 + 16w = 0 Opposite signs on the constants will result in a negative value for c when multiplying the factors. -8h 13n + 6 (6x 3y)2 y = (x 5)(x + 3). = s 25. Answer: Given equation (n 1)(n + 6)(n + 5) = 0 Question 3. (9r2 + 4r 7) + (3r2 3r) MATHEMATICAL CONNECTIONS In Exercises 31 34, write a polynomial that represents the area of the shaded region. Answer: Question 18. n = 2 or n = -18/2 or n = 2 Click on the respective link and kickstart your learnings. Answer: w + 13w + 42, Question 10. Polynomials can have no variable at all. (4a a3 3) + (2a3 5a2 + 8) -x+x+25. The browser covers \(\frac{3}{13}\) of the screen. Find the width of the entrance at ground level. b. the set of whole numbers; addition = (x + 2x + 2) (x 1) 8x 2x 2 (x + 9)(x 9) = (x) (9) s2 15s + 50 Answer: Writing a Product of Linear Factors = (2x) 1 x2 + bx + c 4r r 8r 10. (use paper and pencil methods and . (2x 1) = (2x) + (1) + 2(2x)(1) Question 49. x = 4 x 2x + 8x 16x = 96 It is in the form of (a + b)(a b) = a b x + px + qx + pq. MODELING WITH MATHEMATICS 0. As you can see from the examples above, we are simply adding (or subtracting) two or more terms together. = -35 is less than 1. ERROR ANALYSIS = 10,000 441 The width x of your iris decreases from 4millimeters to 2 millimeters when you enter a dark room. Answer: Factor the polynomial. Answer: y2 100 = y2 10 = (y + 10)(y 10), Question 33. x2 9 HOW DO YOU SEE IT? Please do not post the Answer Keys or other membership content on a website for others to view. (t + 5)2 =t + 5 + 2(t)(5) A web browser is open on your computer screen. MODELING WITH MATHEMATICS z(z + 3) 25(z + 3) = 0 (y + 4)(y + 1) Answer: So, (a + b)(a b) = a b x = -1 or x = -7 Answer: 4a + 6 Question 9. b 8b + 15 = 0 Please dont reverse-engineer the software or printed materials. Question 49. Answer: Legend (Opens a modal) . Answer: Question 44. 8m2 + 30m + 7 In Example 5(a), how does the polynomial change when the longer base is extended by 1 foot? Describe two ways to determine the percent of possible gene combinations that result in green pods. = 140, Question 6. Our state-specific browser-based blanks and complete instructions eliminate human-prone errors. a. A = 4x + 84x + 440. b. units Answer: Find expressions that could represent the dimensions of the room. (x + 8)(x 9) = 0 Thus the polynomial represents the area of the deck. 6x2 + 17x + 7 224 Holt McDougal Algebra 1 CS10_A1_MESK710372_C07.indd 224 3/30/11 11:23:21 PM. (s + 5)(s 5) WHICH ONE DOESNT BELONG? Algebra 1 unit 7 test polynomials and factoring - Determine whether the expression is a polynomial. -2y2 5y 3 -8d + 26d 15, Question 11. So, (y + 6)(y + 4) = y + 10y + 24, Question 6. = (2x 3)(3x + 1). This Polynomials and Factoring Unit Bundle contains guided notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics: Multiplying Binomials (FOIL) and Binomial x Trinomial, Factoring by finding Greatest Common Factor (GCF), Factoring Trinomials (ax2 + bx + c) *By Slip & Slide, Factoring Review (organized by type, then practice with it mixed), Dividing Polynomials by a Binomial (by Factoring). (3s + 5)(5s + 8) = 0 For one jump, your height y (in feet) above the trampoline after t seconds can be represented by y = -16t2 + 24t. So, (6x 3y) = 36x + 9y 36xy. _____ F 34 Simplify. (30 + 3)(30 3) = 30 3 REASONING 3p + 7 = 0 or 3p 7 = 0 or p + 8 = 0 y = -2/315(x + 315)(x 315) The length of a rectangle is 1 inch more than twice its width. b. The patio will cost $10 per square foot. DOWNLOAD ALGEBRA 1 UNIT 7 TEST POLYNOMIALS AND FACTORING AND GET THE ANSWERS Hey, we've all been there! Answer: x 2(\(\frac{2}{3}\))x + \(\frac{2}{3}\) = 0 Question 21. Question 39. Answer: Answer: x(-x + 2) UNIT 7Polynomial Functions. -5t + 3 t 4 + 8t 4r r 7r r 10 So, the perimeter of the stage is 2(x + 16 + x + 11) or 2(2x + 27). (f + 1) The polynomial 400x8 + 600x6 has a degree 8 and is a binomial. \(\left(\frac{2 y^{4}}{y^{3}}\right)^{-2}\) 2 24 A = P(1 + r/2)nt You are saving money to buy an electric guitar. (-3y + 1)(4y2 y 7) (x + 2)(x + 1)(-x) = (x + 2)(-x x) = -x 2x x 2x = -x 3x 2x (m + 6)(m 6) 2 = 4d or 2 = -4d j2 13j + 42 = (j 7)(j 6). Find a pattern in the terms and use it to write a pattern for the cube of a binomial (a + b)3. Factor a perfect square trinomial. Explain your reasoning. 24v + 8v 36 30v 10v + 45v Combine the like terms to add or subtract the polynomials s = -10, Question 32. Answer: (7m + 8n)(7m 8n) Answer: n 5 = 0 or n 7 = 0 = x 4x + 6x 24 -2w + 32w + 72w = 1152 2 . p2 + 2p 35 Answer: RIGOROUS. x(x + 5) 3(x + 5) a. Unit 7 Review. -12y + 8y3 (6x 3y) = (6x) + (3y) 2(6x)(3y) WRITING The highest exponent in the polynomial is called a degree. Given polynomial (-2p + 4) (p2 6p + 8) Each joke worksheet comes with a step-by-step answer key.1. UNIT #2 . So, (4x y) = 16x + y 8xy, Question 4. Answer: = x(x 2) + 1(x 2) (3a + 7) + (a 1) 20x3 + 30x = 10x(2x + 3), Question 30. Factors of 26 are (1, 26), (2, 13) FEEDBACK REQUESTED. Write a trinomial in one variable of degree 5 in standard form. Find the sum or difference. (p + 7) (6p2 + 13p) Answer: Answer: After how many seconds does the paintbrush land on the ground? In Exercises 38, factor the polynomial. (x 2) (-2x + 1) Factoring Special Products Work with a partner. The degree of the polynomial is 2 10a2 13a 3 Given, So, your friend is correct. Answer: (2x2 + 5) + (-x2 + 4) Answer: Question 1. -3x2 x + 2 Answer: Question 45. (x 4)(x 3), d. x + 7x + 12 Answer: x(x 3) + 4a(x 3) n = 2 or \(\frac{2}{3}\)n = -6 or n = 2 Answer: Simplify the expression. Question 43. (a 6) = a + 6 2a(6) In Exercises 4548, factor the polynomial. (y3 + 4) = (y) + 4 + 2y(4) 5.2 Power Functions and Polynomial Functions. 4x2 = 2x You are playing miniature golf on the hole shown. = y(3y + 8) 5(3y + 8) e. (x 2)2 a. 6x + 8 = 26x A = (x 15) y 62 = 61(x 1) Answer: COMPARING METHODS p(x) = 1/2 x + 1/2 Answer: Polynomials Vocabulary! Question 8. Question 54. (-12 n)2 3x(2x y) + 4y(2x y) Polynomials And Factoring (Algebra 1 Curriculum - Unit 7) Polynomials and Factoring (Algebra 1 Curriculum - Unit 7) | All Things AlgebraDISTANCE LEARNING UPDATE: This unit now . = 6s4 3t, Find the product. Answer: 4r = 0 or r + 7 = 0 The degree of the polynomial is 3 A = (6 x) (a2 3ab + b2) + (-a2 + ab + b2) Answer: Question 28. (x2 x 2) + (7x2 x) (p + 3)(p 8) = p(p 8) + 3(p 8) The table shows one method of finding the product of two binomials. (x + 10)(x 10) 9r2 36r 45 n 4 = (n + 4)(n 4) Thi. j2 13j + 42 When you subscribe, we give you permission (a Single User License) to use our copyrights and trade secrets and those we license from others, according to our Terms & Conditions. -16(1) 16(1) 3 Is your friend correct? Question 3. c. (x + 2)(2x 1) v 7v + 6v 42 n 7n 5n + 35 a. is not factorable A = (p + 1)(2p 6) h = x 2 -6 2 = -8 Answer: In Exercises 2328, solve the equation. 4x + 11x 3 = 0 So, the degree is 4. (b 4ac = (-17) -4(39)(-376) A = (6 + x 2.6(x)) length = 2x + 4 Use algebra tiles to factor each polynomial modeled by the tiles. Answer: p(x) q(x) = 1 x = 0 or x + 3 = 0 or x 3 = 0 (4c + 4d) = (4c) + (4d) + 2(4c)(4d) Question 33. Answer: x(2x 1) + 2(2x 1) r = 0 or r = 10 Write an expression that represents the area being paved. v = 7, -6, Question 9. The magician wishes to have the area of the stage be at least 20 times the area of the trapdoor. A cardboard box in the shape of a rectangular prism has the dimensions shown. Solve the equation. the coefficient is 5, -3 We know its nice to share, but please dont share your membership content or your login or validation info. Question 5. Answer: 2(x 1) + 3(x + 2) Take 3y as common and cancel them. Combined area of the photo and the frame is 4x + 84x + 440 So, 4(h + 6) (h 2) = 3h + 25. Question 47. Answer: Question 11. p(p + 7) 5(p + 7) Question 6. = (x + 1)(3x + 2), b. 2m2 50 x2 + 9x + 8 Answer: Question 40. Answer: Question 56. 24 = 24 Answer: Question 46. w = 4, 4, Question 7. b. It is in the form of (a b) = a + b 2ab Answer: So, the factor pairs of 18 are 1, 2, 3, 6, 9, 18. Question 3. A penguin leaps out of the water while swimming. OPEN-ENDED = x(x) + x(1) x(x) x(1) You deposit $1000 in an account that earns interest compounded annually. examples 1. x + 5x 3x 15 x + 4x + 3x + 12 ERROR ANALYSIS Then classify the polynomial by the number of terms. = 4x 16, Question 15. c. x3 + 6x2 + 9x (4q + 3)(q + 2) = 0 j. x 3x + 2x = x(x 3x + 2) = x(x 2x 1x + 2) = x(x(x 2) 1(x 2)) = x(x 2)(x 1) E ( 2u + \(\frac{1}{2}\))( u \(\frac{3}{2}\)) Answer: Answer: Arrange algebra tiles for the given trinomial x2 + bx + c such that the model is a rectangular array. y = 3x 3 (10 \(\frac{1}{3}\))(10 + \(\frac{1}{3}\)) = 10 \(\frac{1}{3}\) -3t2 + 11t 6 Finding Binomial Factors y = |x| + 4 = 6[y(y 3) 1(y 3)] = (5x 1), c. 25x2 1 A rectangular swimming pool is bordered by a concrete patio. y 10y + 3y 30 = 0 It is in the form of (a + b) = a + b + 2ab (5s + 6)(s 2) Step 2: x + x + x + x + 1 + 1 1 1 1 1 1 For better learnings, we have curated Big Ideas Math Book Algebra 1 Ch 7 Polynomial Equations and Factoring 7.1 to 7.8 Exercises Questions, Chapter Review, Chapter Test, Cumulative Assessment, etc. = 208, Factor the polynomial. Answer: (3e2 5e + 7)(6e + 1) Factor a difference of squares. MODELING WITH MATHEMATICS Which is different? = 7b(2b + 1) 2(2b + 1) = 0 The absolute value of the difference of the two polynomials represents the vertical distance between points on the lines with the same x-value. One of the properties in Exploration 3 is called the Zero-Product Property. Write the expression modeled by the algebra tiles in each step. 2x(3x2+ 2x 4) = 3 (2x2 4x+ 7) = 2x(3x2+ 2x 4) = 6x2 12x+ 21 6 =x3+ 4x2 8x c. 3x(5x+ 4) 4 (x2 3x) d. 8 (a2 2a+ 3) 4 (3a2+ 7) (only multiply Answer: In Exercises 914, factor the polynomial. w 1w 3w + 3 = -4x 8 V = lwh Answer: Question 10. 2x 2 + 3x + 6 (x + x + 7)(x + x + 7) = (2x + 7) Write this expression. -5y2 22y 8 18v2 15v 18 Question 3. = (2m + 7)(4m + 1), Question 12. Answer: Question 22. Answer: 47 44 pre-college algebra co req factoring polynomials greatest common factor the greatest common factor (gcf) of polynomials is the largest polynomial that divides Skip to document Ask an Expert Question 1. y + 2x + xy + 2y d2 10d + 25 x = -6, -4, 4 j(j 7) -6(j 7) t = 0 or t = -2 Answer: Find a value for w so that the equation has (a) two solutions and (b) three solutions. (2b + 1)(7b 2) = 0 (-3n2 + n) (2n2 7) Matching Equivalent Forms of an Equation -x + x 4 Essential Question How can you solve a polynomial equation? Answer: z + 4z 12 = -x 2x The x-axis represents the ground. Question 53. (a 6)2 Answer: 3s = -5 or 5s = -8 = t 7t + 11t 2. x2 3x + 4ax 12a All answer keys are included. Factor a trinomial of the form . 1. Give an example. (x2 + 6x 5) + (2x2 + 15) 8m2n4 y = x + 15 x > 0 The cost (in dollars) of making b necklaces is represented by 8b + 6. x2 + 6x 5 + 2x2 + 15 d. (2x 3x) (x2 2x + 4) v2 5v + 4 l = 24 + 2x Explain how the letters of the word FOIL can help you to remember how to multiply two binomials. x(x 3) + 1(x 3) = 0 x = 0 or x = 1 = 212, Question 14. The Gateway Arch in St. Louis can be modeled by y = \(\frac{2}{315}\)(x + 315)(x 315), where x and y are measured in feet. How can you add and subtract polynomials? The layout of the assessment itself is not editable. x = -7/3, -1/2, Question 28. Question 52. Textbook Authors: Hall, Prentice, ISBN-10: 0133500403, ISBN-13: 978--13350-040-0, Publisher: Prentice Hall m = 123 62/2 1 6m(m + 2) = 0 Easily fill out PDF blank, edit, and sign them. y = 2, -15, Question 8. s2 + 3s 40 -16d + 3d 3d + 2 Answer: 1. x2 - 36 2. a2b2 - 100 3. Use algebra tiles to factor each polynomial modeled by the tiles. The coefficient is 2.8 and 1. w 3 = 0 or w 1 = 0 Web 7 answer key in pdf format.wilson factoring polynomials by grouping unit 8 quadratics by factoring unit #7 polynomials lesson # 3 gina wilson all things algebra 2017 unit 3 :. = 1/2 (x 7)[x + (x + 11)] Without factoring, determine which of the graphs represents the function g(x) = 21x2 + 37x + 12 and which represents the function h(x) = 21x2 37x + 12. N = -0.028t3 + 0.06t2+ 0.1t + 17 = (3x) + (1) + 2(3x)(1) Write a polynomial that represents the volume of the birdhouse. WRITING Answer: Answer: Given polynomial 16h2 49 The numbers 0 and 1 have special properties that are shared by no other numbers. 2x = 0 or x + x 10 = 0, Solve the equation. n2 81 = 0 Unit 6 Exponential Functions. You can model the entrance to a mine shaft using the equation y = \(\frac{1}{2}\)(x + 4)(x 4), where x and y are measured in feet. d(d 5) 5(d 5) Area of a trapezoid = 1/2 h [b1 + b2] In Exercises 38, solve the equation. Question 49. 1. 49s + 35t USING STRUCTURE Answer: Question 43. 6 -7 = c y 5y + 3y 15 = 0 Answer: Question 34. 5x + x 4 2 = 0 2x = y + 2 \(\sqrt{81}\) = 9. a2 + 11ab 26b2 c. x3 + 6x2 + 9x= x(x + 6x + 9) = x(x + 3), Factor the polynomial by grouping. So, the solution is p = 9. Answer: Question 3. Identifying Parts of an Expression . Factor out the GCF of a polynomial. 2x(x + 1/2) = 10 The expression \(\frac{4}{3}\) r3 represents the volume of a sphere with radius r. Why is this expression a monomial? Answer: Squaring on both sides y = (x + 1)(x + 7) 15 5 = 75 So, (3m + n) = 9m + n + 6mn, Find the product. x = -1, -8, Factor the polynomial. length = x + 8 Example: xy4 5x2z has two terms, and three variables (x, y and z) Answer: Question 13. y = 9 (\(\frac{1}{3}\))x (z \(\frac{5}{3}\)) (z \(\frac{2}{3}\)) What is its degree? Answer: Question 20. It is in the form of (a + b)2 = a + 2ab + b So, x = 3 Is your friend correct? Essential Question How can you recognize and factor special products? d = -7, Question 14. x(x 2) + 3(x 2) Your friend claims to be able to use a special product pattern to determine that (4\(\frac{1}{3}\))2 is equal to 16\(\frac{1}{9}\). V = h(5h h + 36) z(z + 7) + 3(z + 7) 2. The length of the base of the Parthenon is 8 meters more than twice its width. c3 7c2 + 12c = 0 Apply the factoring strategy to factor a . MATHEMATICAL CONNECTIONS (2q 6)2 Answer: x(x 4) 3(x 4) by tfgiles4107. 4x -20x + 1x 5 -20.5 is same as -20.5x0 since anything to the zero power is equal to 1. = x + 3x 16x + 12. Given, coefficient is 2 s = -3, 20. Please click the link below to submit your verification request. (4s4 + 2st + t) + (2s4 2st 4t) Answer: Question 30. (4x-5 16)(3x 81) = 0 x(x 1) -2(x 1) (2x + 7)(2x 7) = 0 Answer: 4x 1 Explain your reasoning. Answer: Unit 7 Polynomials And Factoring Gina Mount Wilson Answer Key. 9th grade . x = -4 or x = 4 Given polynomial Explain your strategy. = m(m 4m + 2m 8) Write a polynomial in standard form that represents the area covered by the hour hand in one rotation. Find the width of the tunnel at ground level. Question 3. Answer: b. Wondering how to ace up your preparation for Chapter 7 Polynomial Equations and Factoring? (2x + 1)(2x 1) = (2x) (1) (y + 6)(y + 4) 4y 7y 16y + 28 = 0 10w2 31w + 15 5x2 5x 30 = 0 Each of two dogs has one black gene (B) and one white gene (W). -5k2 22k + 15 Practical Algebra Lessons Purplemath. When you add 0 to a number n, you get n. = 841, Question 30. Answer: Question 48. It is in the form of (a + b) = a + b + 2ab -3x 3x + 2x + 2 It was a great help. Answer: Use the polynomial in part (a) to fond the area when x = 15. Describe two ways to find the product of two binomials. 6 = \(\frac{c}{-7}\) = x + 5x + 3x + 15 f. (x 6)(x 1) = 0 l = 2(3) 1 = 5. (x + 16)(x + 11) k + 25 does not belong with the other three. z 7z + 3z 21 ERROR ANALYSIS In Exercises 33 and 34, describe and correct the error in factoring the polynomial completely. The width of a box in the shape of a rectangular prism is 4 inches more than the height h. The polynomials represent the heights (in feet) of the balls after t seconds. Because P(x) be a factor of x7+1=(10000001) . = 4m(2m + 7) + 1(2m + 7) = x + 4x 2x 8 Question 3. DIFFERENT WORDS, SAME QUESTION If you already have a plan, please login. Answer: x2 + 7x + 6 Answer: Question 46. Is the function increasing or decreasing for increasing values of x? Answer: y = 30/5 Find the width. The coefficient of the polynomial is -8 Find both answers. Answer: The cost (in dollars)of making b bracelets is represented by 4 + 5b. n2 12n + 35 The number of family memberships at the fitness center in m months is represented by 52 + 6m. Write the polynomial in a standard form that represents the balance of your account after 2 years. Answer: Answer: Question 48. = 9z 25, Question 13. 8y = 0 or y 3 = 0 All Things Algebra Unit 7 Answer Key Make these fast steps to change the PDF Unit 7 polynomials and factoring homework 1 answer key pdf online free of charge: Register and log in to your account. U = -0.38t2 + 1.5t + 42 a. c = -42 = m(m 4)(m + 2), Solve the equation. Answer: (3z 5)(3z + 5) Answer: w = w w = 16 or w = -6 = (75)(3) Factors of 75 are 1, 3, 5, 15, 25 and 75 The area (in square meters) of the surface of an artificial lake is represented by x2. Write a polynomial that represents the volume of the container. 6m2 + 12m = 0 = 8(k(k + 5) + 5(k + 5)) 2 n = 0 or 6 + \(\frac{2}{3}\)n = 0 or n 2 = 0 Answer: HOW DO YOU SEE IT? Answer: 403408), Factor the polynomial completely. = (47 47) (44 44) What do you know about m and n when c < 0? 2x + 5x 4x 10 = 0 To read the Single User License Agreement, please clickHERE. In pea plants, any gene combination with a green gene (G) results in a green pod. Factoring Polynomials Gina Wilson Worksheet 2. (h 5)(h 8) 0.5B + 0.5W Write a polynomial that represents the area of the football field. x + x 1, Question 6. x = 20 -5k2 22k + 15 e = E = 2, Writing a Conjecture (-5g 2h)(-5g + 2h) MATHEMATICAL CONNECTIONS Unit 5 Lesson 1 Polynomial Functions Answers Unit 5 Lesson 1 Polynomial Functions Answers . = y(y + x) + 2(x + y) Read about how we use cookies and how you can control them in our. MODELING WITH MATHEMATICS Answer: = 8[x(x 1) 6(x 1)] y + 2 = 0 or y 6 = 0 = 441 The prime factorization of 96 are 2 2 2 2 2 3.
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