Unit 8 Polynomials and Factoring Review

Polynomial Basics

1

How many terms does this polynomial have:

8xy² + 9xy - 13²y + 22

4 terms

2

What is the leading coefficient:

-5m² - 14m - 17

-5 

3

Write in standard form:

8 + 5k³ + 7k -3k² 

5k³ - 3k² + 7k + 8

4

Classify by degree and number of terms:(the fancy words)

2m⁴-7m²-5m+1

Quartic polynomial

5

Classify by degree and number of terms:(the fancy words)

2x² - 14x + 7

quadratic trinomial

Multiplying Polynomials

1

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

2

Multiply the Polynomials:

5x³(x + 2)

5x⁴ + 10x³

3

Multiply the Polynomials:

(2m - 1)(m + 2)

2m² + 3m - 2

4

Multiply the Polynomials:

(4n - 1)(3n + 4)

12n² + 13n - 4

5

Multiply the Polynomials:

(d + 3)(d² - 4d + 1)

d³ - d² -11d + 3

Factoring GCF/ Special Products

1

Find the GCF:

18xy⁴z³ and 30x⁴y⁴

6xy⁴

2

Factor using GCF

30x-42

6(5x-7)

3

Factor by using GCF

5a³+2a²

a²(5a+2)

4

Factor out the GCF

18n⁴+42nm+6n

6n(3n³+7m+1)

5

Factor out the GCF:

3a^3b^2c-9a^2b^3c^2+15ab^4c^3

3ab^2c(a^2-3abc+5b^2c^2)

Factoring

1

Factor:

p² +2p -35

(p-5)(p+7)

2

Factor:

z² - 4z - 21

(z+3)(z-7)

3

Factor:

a^2+10a+24

(a+6)(a+4)

4

Factor:

y^2-17y+72

(y-9)(y-8)

5

Factor out GCF First, then factor the trinomial:

2b^2+10b+12

2(b+3)(b+2)

Dividing Polynomials

1

Find the quotient:

(6x+9)/3

2x+3

2

find the quotient:

(8c^3+21c^2+3c)/(3c)

8a²-2a+5

3

Find the quotient:

(6a^2b-12ab^2)/(-2ab)

-3a+6b

4

Find the quotient:

(28x^5y^4z^3+8x^4y^3z^2)/(4x^2y^2z^2)

7x³y²z+2x²y

5

Simplify expression completely:

((m^2n^2-mn)(m^2n^2+mn))/(mn)

m³n³-mn