CK-12 Basic Algebra Concepts 1
9.1 Polynomials in Standard Form Answers
1. Polynomial - an expression made with constants, variables, and positive integer exponents of the variables.
2. Monomial - a one-termed polynomial.
3. Degree - The degree of a polynomial is named by identifying the largest exponent of a single term.
4. Leading coefficient – the first coefficient in the first term of a polynomial.
5. It is a polynomial because it has constants, variables and terms
6. It is a polynomial because it has constants, variables and terms
7. It is a monomial because it has constants, variables
8. It is a polynomial because it has constants, variables and terms
9. 2 – 3, 1
10. 194 + 52 − − 10, 4
11. 33 − 4 − 8, 3
12. 58 − 73 − 16, 8
13. 83 − 52 + 2 − 5, 3
14. −94 + 2 + 12, 4
Chapter 9 – Polynomials and Factoring Answer Key
CK-12 Basic Algebra Concepts 2
9.2 Addition and Subtraction of Polynomials
Answers
3. −2 + 11 − 12
5. 6.92 − 4.82 + 3.1 + + 2
6. −102 − 3 + 9
7. −62 + 2 − 12
9. −82 − 5 + 5
11. 2 +
12. 4 + 2
13. 2 − 22
CK-12 Basic Algebra Concepts 3
9.3 Multiplication of Monomials by Polynomials
Answers
CK-12 Basic Algebra Concepts 4
9.4 Multiplication of Polynomials by Binomials
Answers
8. 273 + 8
10. 33 + 42 − 59 − 20
11. 22 + 14 + 20
CK-12 Basic Algebra Concepts 5
9.5 Special Products of Polynomials
Answers
Square of a Binomial - ( + )2 = 2 + 2 + 2, ( − )2 = 2 − 2 + 2
Sum and Difference Formula - ( + )( − ) = 2 − 2
1. 2 + 18 + 81
2. 2 − 2 + 1
3. 42 + 24 + 36
4. 92 − 42 + 49
5. 492 + 112 + 64
6. 814 + 1082 + 36
7. 4 − 22 + 1
8. 6 + 83 + 16
CK-12 Basic Algebra Concepts 6
12. 164 + 822 + 4
13. 642 − 48 + 9
CK-12 Basic Algebra Concepts 7
26. 8051
27. 361
28. 3136
29. 721,824
30. 999,996
31. 1584
CK-12 Basic Algebra Concepts 8
9.6 Monomial Factors of Polynomials
Answers
2. (3 + 12 + 16
7. 12(1 + 2 + 32)
CK-12 Basic Algebra Concepts 9
9.7 Zero Product Principle
Answers
1. The only way a product is zero is if one or both of the terms are zero.
2. Because they are not set equal to zero.
3. They are a sum, not a product
4. The first factor is a fraction that cannot be set equal to zero.
5. They are a difference, not a product.
6. It is not completely factored.
7. 0, 12
CK-12 Basic Algebra Concepts 10
13. 0, −9, 20
CK-12 Basic Algebra Concepts 11
9.8 Factorization of Quadratic Expressions
Answers
CK-12 Basic Algebra Concepts 12
10. (−9 + −1)(3 + −1)
11. (−13 + −1)(6 + −1)
12. (−8 + −1)(4 + −1)
13. (−3 + −1)(15 + −1)
14. (−5 + −1)(10 + −1)
15. (−5 + −1)(8 + −1)
16. (−7 + −1)(8 + −1)
17. −1(1 + )(1 + )
18. (3 + −1)(8 + )
CK-12 Basic Algebra Concepts 13
19. (−12 + )(6 + −1)
20. (−15 + )(10 + −1)
21. (12 + )(9 + )
22. (−6 + )(5 + −1)
23. (−16 + −1)(4 + −1)
24. (−3 + −1)(20 + −1)
CK-12 Basic Algebra Concepts 14
9.9 Factor Polynomials Using Special Products
Answers
11. (10 + )(10 + −1)
Chapter 9 – Polynomials and Factoring Answer Key
CK-12 Basic Algebra Concepts 15
13. (2 + 3)(−2 + 3)
14. (7 + 5)(−7 + 5)
15. (5 + 6)(5 + −6)
16. (4 + 9)(4 + −9)
17. = 5, 6
18. = −7, 3
CK-12 Basic Algebra Concepts 16
9.10 Factoring by Grouping
7. (3 + 4)(82 − 1)
8. (2 + 3)(2 + 2)
11. (52 + 7)( − 1)
12. (3 + 7)( + 3)
13. (4 + 20)( + 8)
14. (10 + 6)( + 4)
CK-12 Basic Algebra Concepts 17
9.11 Factoring Completely
5. −5(2 + )(2 + )
7. (−7 + )(3 + −1)
10. 3(1 + 2)(1 + 2)
12. 1 = 15, 2 = 12
13. 8
14. 2 2
Chapter 9 – Polynomials and Factoring Answer Key
CK-12 Basic Algebra Concepts 18
9.12 Probability of Compound Events
Answers
1. Independent events are occurrences where the outcome of the second event is not
affected by the outcome of the first event.
2. Independent
3. Dependent
4. Independent
5. Independent
6. 1
36
7. Mutually Exclusive is when two events cannot happen at the same time.
8. Mutually Exclusive
CK-12 Basic Algebra Concepts 19
13. Mutually Exclusive
14. a. 2