Multiplying and Factoring Polynomials

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

What is the degree of the polynomial:

9ab^{2 +} 2a²b³c + 6b⁴c² - 5ab⁵c - 13

7th degree

4

Write in standard form:

8 + 5k³ + 7k -3k² 

5k³ - 3k² + 7k + 8

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:

(x - 3)(x + 2)

x² - x - 6

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

Factor using GCF

30x-42

6(5x-7)

2

Factor by using GCF

5a³+2a²

a²(5a+2)

3

Factor:

2x² - 8

2(x+2)(x-2)

4

Factor:

4p² - 256

4(p+8)(p-8)

5

Factor out the GCF

18n⁴+42nm+6n

6n(3n³+7m+1)

Factoring

1

Factor:

p² +2p -35

(p-5)(p+7)

2

Factor:

z² - 4z - 21

(z+3)(z-7)

3

Factor:

5y² + 22y + 8

(5y+2)(y+4)

4

Factor:

x² - 3x + 4ax - 12a

(x+4a)(x-3)

5

Factor:

n³ - 9n

n(n+3)(n-3)

Solve by Factoring

1

Solve by factoring:

x² - 25=0

x=-5 and x=5

2

Solve by factoring:

3x² - 3x - 60=0

x=-4 and x=5

3

Solve by factoring:

-5x² + x = -4

x=-4/5 and x=1

4

Solve by factoring:

30x² - 4 = 2x

x=2/5 and x=-1/3

5

Solve by factoring:

5n² - 40n = 0

n=0 and n=8