Mathmatics1

Unit 2: Working with Polynomials 85

Practice

Use the list below to identify each polynomial. Write the word on the line provided.

binomial monomial trinomial

________________________ 1. 3b2 – b

________________________ 2. 4x5

________________________ 3. 5t2 – 3t5

________________________ 4. 5x3 – 4x2 + 3x

________________________ 5. 3r2st2

________________________ 6. x – y + 3

Unit 2: Working with Polynomials86

Practice

Use the list below to identify each polynomial. Write the word on the line provided.

binomial monomial trinomial

________________________ 1. 3x3 – 2x2 + 1

________________________ 2. 4xy2z

________________________ 3. a – b + 2

________________________ 4. 2a2 – a

________________________ 5. 6b2

________________________ 6. 3x2 – 5y2

Unit 2: Working with Polynomials 87

Practice

Match each definition with the correct term. Write the letter on the line provided.

______ 1. a monomial or sum of monomials

______ 2. a polynomial with only one term

______ 3. an exponent; the number that tells how many times a number is used as a factor

______ 4. any symbol, usually a letter, which could represent a number

______ 5. a polynomial with exactly three terms

______ 6. a collection of numbers, symbols, and/or operation signs that stands for a number

______ 7. a polynomial with exactly two terms

______ 8. the numbers in the set {1, 2, 3, 4, 5, …}

A. binomial

B. expression

C. monomial

D. natural numbers

E. polynomial

F. power (of a number)

G. trinomial

H. variable

Unit 2: Working with Polynomials 101

Practice

Write each product as a polynomial in simplest form.

Remember: Multiply the coefficients and add the exponents.

Example: (7a2)(5a3b4) = 35a5b4

1. (6t)(-3t3) =

2. (5x)(-x4) =

3. (-6r2s)(4r2s3) =

4. (-5a)(ab3)(-3a2bc) =

5. (y2z)(-3x2z2)(-y4z) =

6. -a2(ab2)(3a)(-2b3) =

Unit 2: Working with Polynomials102

7. (-t)2(2t2)(5t)2 =

Hint: Notice with (-t)2 and (5t)2, the exponent 2 is placed on the outside of the grouping symbols, the parentheses. Use the distributive property and raise every term in the parentheses to the exponent.

Example: (-t)2 = t2

(5t)2 = 25t2

8. (3x2)(-5x3y2)(0)(-4y)2 =

Hint: Notice the zero (0). The zero property of multiplication, also known as the zero product property, states that any number multiplied by 0 is 0.

Zero Property of Multiplication or Zero Product Property

For all numbers a and b, if ab = 0, then

a = 0 and/or b = 0.

Unit 2: Working with Polynomials 103

Practice

Write each product as a polynomial in simplest form.

1. (8x)(-2x2) =

2. (5a)(-a6) =

3. (-4x2y)(3x3y2) =

4. (-6b)(ab4)(-4a2bc2) =

Unit 2: Working with Polynomials104

5. (x3y2)(-2x2y)(-x4y2) =

6. -s3(s2t2)(4s)(-2t4) =

7. (-a)2(4a2)(3a)2 =

8. (6x)2(-2x2y3)(0)(-2x)2 =

Unit 2: Working with Polynomials 149

Practice

Use the list below to write the correct term for each description on the line provided.

binomial coefficient composite number factor

like terms monomial polynomial prime number

rational expression simplest form

(of an expression) trinomial

________________________ 1. a number whose only factors are 1 and the number itself

________________________ 2. the number part in front of an algebraic term signifying multiplication

________________________ 3. a polynomial with exactly 2 terms

________________________ 4. a polynomial with only 1 term

________________________ 5. polynomials with exactly the same variable combinations.

________________________ 6. a polynomial with exactly 3 terms

________________________ 7. any rational expression with no variable in the denominator

________________________ 8. a polynomial that contains no grouping symbols (except a fraction bar), and all like terms have been combined

________________________ 9. one of the numbers multiplied to get a product

________________________ 10. a fraction whose numerator and/or denominator are polynomials

________________________ 11. a whole number that has more than two factors