I. Mixed Review II. Challenge Problems III. Answer Key
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I. Mixed Review II. Challenge Problems III. Answer Key Web Resources Adding and Subtracting Polynomials www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php Multiplying Polynomials www.mathwarehouse.com/algebra/polynomial/how-to-multiply-polynomials.php Multiplying a Polynomial by a Monomial www.mathwarehouse.com/algebra/polynomial/multiply-polynomial-by-monomial.php How to Multiply Binomials (FOIL) www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php Multiply Polynomials by Polynomials www.mathwarehouse.com/algebra/polynomial/multiplying-polynomials-bypolynomials.php © www.MathWorksheetsGo.com All Rights Reserved Commercial Use Prohibited Terms of Use: By downloading this file you are agreeing to the Terms of Use Described at http://www.mathworksheetsgo.com/downloads/terms-of-use.php . Graph Paper Maker (free): www.mathworksheetsgo.com/paper/ Online Graphing Calculator(free): www.mathworksheetsgo.com/calculator/
I. Mixed Review Add or subtract. 1. (3x3 + 4x2 + 1) + (2x2 + 10) 3. (-8x3 + 4x – 1) – (4x2 – x)
2. (-4x2 + 3x – 1) – (4x + 2)
5. (9x5 – 7x3 + x) + (6x4 + 9x3)
4. (7x3 + 6x2 + x – 1) + (9x3 + 4x2 – x + 10) 6. (5x2 – 7x + 10) – (6x2 + 8x – 5)
7. (10x2 – 8x + 10) – (6x2 + 7x + 10)
8. (4x4 + 3x3 + 2x2 + x) + (3x4 – 4x3 + 2x2 – x)
9. (8x3 + 5x + 1) + (10x3 + 4x2)
10. (17x5 + 5x3 + x) – (6x5 + 4x3 + x)
Multiply. 11. 2x(4x2 + 5x + 10)
12. 3x2(2x2 + 2x + 1)
13. (x + 1)(x + 10)
14. (x + 2)(x – 2)
15. (x2 + 1)(x2 – 5)
16. (x + 9)(x2 + 7x)
17. (x + 1)(x2 + 5x + 10)
18. (x2 + 5)(x3 + 2x + 1)
Divide. 19. (x2 + 10x + 16) (x + 2)
20. (x3 – 4x2 + 7x – 6) (x – 2)
21. (x3 – x2 + 8x – 8) (x – 1)
22. (x3 + 13x2 + 39x – 5) (x + 5)
23. (x3 – 27) (x – 3)
24. (x3 – 3x2 – 9x) (x – 5)
25. (x3 – 7x2 – 17x – 9) (x + 1)
26. (12x3 + 23x2 + 10x + 2) (3x + 2)
II. Challenge Problems 27. Add: (3x3y3 + 2x2y + xy2 + y3) + (4x3y3 – 4x2y – 5xy2 – 6y3) _________________________________________________________
28. P(x), D(x), Q(x) and R(x) are polynomials. If P(x) is divided by D(x), the quotient is Q(x) with remainder R(x). What is the value of P(x) in terms of D(x), Q(x) and R(x)? _________________________________________________________ _________________________________________________________ 29. If the base of a triangle is given by the expression (3x2 + 4x) and the height of the triangle is given by the expression (4x2 + 4x + 6), what is an expression for the area of the triangle, in terms of x? _________________________________________________________ 30. Correct the Error There is an error in the student work shown below: Question: Multiply (3x2 + x – 8)(x – 1). Solution: (3x 2 x 8)(x 1)
3x 3 x 2 8x 3x 2 x 8 3x 3 4x 2 9x 8 The answer is 3x3 – 4x2– 9x + 8. What is the error? Explain how to solve the problem. _________________________________________________________ _________________________________________________________
III. Answer Key 1. 3x3 + 6x2 + 11 2. -4x2 + 7x – 3 3. -8x3 – 4x2 + 5x – 1 4. 16x3 + 10x2 + 9 5. 9x5 + 6x4 + 2x3 + x 6. –x2 – 15x + 15 7. 4x2 – 15x 8. 7x4 – x3 + 4x2 9. 18x3 + 4x2 + 5x + 1 10. 11x5 + 9x3 11. 8x3 + 10x2 + 20x 12. 6x4 + 6x3 + 3x2 13. x2 + 11x + 10 14. x2 – 4 15. x4 – 4x2 – 5 16. x3 + 16x2 + 63x 17. x3 + 6x2 + 15x + 10 18. x5 + 7x3 + x2 + 10x + 5 19. x + 8 20. x2 – 2x + 3 21. x2 + 8 22. x2 + 8x – 1 23. x2 + 3x + 9 24. x2 + 2x + 1 remainder 5 25. x2 – 8x – 9 26. 4x2 + 5x remainder 2 27. 7x3y3 – 2x2y – 4xy2 – 5y3 28. P(x) = D(x)Q(x) + R(x) 29. 6x4 + 14x3 + 26x2 + 24x 30. The student incorrectly added +x2 and -3x2; the answer should be 3x3 – 2x2 – 9x + 8.
I. Mixed Review II. Challenge Problems III. Answer Key Web Resources Adding and Subtracting Polynomials www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php Multiplying Polynomials www.mathwarehouse.com/algebra/polynomial/how-to-multiply-polynomials.php Multiplying a Polynomial by a Monomial www.mathwarehouse.com/algebra/polynomial/multiply-polynomial-by-monomial.php How to Multiply Binomials (FOIL) www.mathwarehouse.com/algebra/polynomial/foil-method-binomials.php Multiply Polynomials by Polynomials www.mathwarehouse.com/algebra/polynomial/multiplying-polynomials-bypolynomials.php © www.MathWorksheetsGo.com All Rights Reserved Commercial Use Prohibited Terms of Use: By downloading this file you are agreeing to the Terms of Use Described at http://www.mathworksheetsgo.com/downloads/terms-of-use.php . Graph Paper Maker (free): www.mathworksheetsgo.com/paper/ Online Graphing Calculator(free): www.mathworksheetsgo.com/calculator/
I. Mixed Review Add or subtract. 1. (3x3 + 4x2 + 1) + (2x2 + 10) 3. (-8x3 + 4x – 1) – (4x2 – x)
2. (-4x2 + 3x – 1) – (4x + 2)
5. (9x5 – 7x3 + x) + (6x4 + 9x3)
4. (7x3 + 6x2 + x – 1) + (9x3 + 4x2 – x + 10) 6. (5x2 – 7x + 10) – (6x2 + 8x – 5)
7. (10x2 – 8x + 10) – (6x2 + 7x + 10)
8. (4x4 + 3x3 + 2x2 + x) + (3x4 – 4x3 + 2x2 – x)
9. (8x3 + 5x + 1) + (10x3 + 4x2)
10. (17x5 + 5x3 + x) – (6x5 + 4x3 + x)
Multiply. 11. 2x(4x2 + 5x + 10)
12. 3x2(2x2 + 2x + 1)
13. (x + 1)(x + 10)
14. (x + 2)(x – 2)
15. (x2 + 1)(x2 – 5)
16. (x + 9)(x2 + 7x)
17. (x + 1)(x2 + 5x + 10)
18. (x2 + 5)(x3 + 2x + 1)
Divide. 19. (x2 + 10x + 16) (x + 2)
20. (x3 – 4x2 + 7x – 6) (x – 2)
21. (x3 – x2 + 8x – 8) (x – 1)
22. (x3 + 13x2 + 39x – 5) (x + 5)
23. (x3 – 27) (x – 3)
24. (x3 – 3x2 – 9x) (x – 5)
25. (x3 – 7x2 – 17x – 9) (x + 1)
26. (12x3 + 23x2 + 10x + 2) (3x + 2)
II. Challenge Problems 27. Add: (3x3y3 + 2x2y + xy2 + y3) + (4x3y3 – 4x2y – 5xy2 – 6y3) _________________________________________________________
28. P(x), D(x), Q(x) and R(x) are polynomials. If P(x) is divided by D(x), the quotient is Q(x) with remainder R(x). What is the value of P(x) in terms of D(x), Q(x) and R(x)? _________________________________________________________ _________________________________________________________ 29. If the base of a triangle is given by the expression (3x2 + 4x) and the height of the triangle is given by the expression (4x2 + 4x + 6), what is an expression for the area of the triangle, in terms of x? _________________________________________________________ 30. Correct the Error There is an error in the student work shown below: Question: Multiply (3x2 + x – 8)(x – 1). Solution: (3x 2 x 8)(x 1)
3x 3 x 2 8x 3x 2 x 8 3x 3 4x 2 9x 8 The answer is 3x3 – 4x2– 9x + 8. What is the error? Explain how to solve the problem. _________________________________________________________ _________________________________________________________
III. Answer Key 1. 3x3 + 6x2 + 11 2. -4x2 + 7x – 3 3. -8x3 – 4x2 + 5x – 1 4. 16x3 + 10x2 + 9 5. 9x5 + 6x4 + 2x3 + x 6. –x2 – 15x + 15 7. 4x2 – 15x 8. 7x4 – x3 + 4x2 9. 18x3 + 4x2 + 5x + 1 10. 11x5 + 9x3 11. 8x3 + 10x2 + 20x 12. 6x4 + 6x3 + 3x2 13. x2 + 11x + 10 14. x2 – 4 15. x4 – 4x2 – 5 16. x3 + 16x2 + 63x 17. x3 + 6x2 + 15x + 10 18. x5 + 7x3 + x2 + 10x + 5 19. x + 8 20. x2 – 2x + 3 21. x2 + 8 22. x2 + 8x – 1 23. x2 + 3x + 9 24. x2 + 2x + 1 remainder 5 25. x2 – 8x – 9 26. 4x2 + 5x remainder 2 27. 7x3y3 – 2x2y – 4xy2 – 5y3 28. P(x) = D(x)Q(x) + R(x) 29. 6x4 + 14x3 + 26x2 + 24x 30. The student incorrectly added +x2 and -3x2; the answer should be 3x3 – 2x2 – 9x + 8.
