Deck 5: Section 2: Factoring

Question 1

Factor out the opposite of the greatest common factor.
10z³ - 2z²

Answer 1

-2z²(-5z + 1)

Question 2

Factor the given polynomial completely. If the polynomial is prime, say so.
c³ + cd + 3c² + 3d

Answer 2

(c + 3)(c² + d)

Question 3

Factor the given polynomial completely.
x⁴ + y⁴

Answer 3

The polynomial is prime.

Question 4

Factor the given polynomial completely.
7p²q - 28pq + 21q

Question 5

Factor out the greatest common factor.
(y - 6)4 + (y - 6)y

Question 6

Factor.
9y² - 100

Question 7

Factor.
q² + 6qr + 36r²

Question 8

Factor.
8x³ - 27

Question 9

Factor completely.
8u³v - 392uv

Question 10

Find the prime factorization.
115

Question 11

Find the greatest common factor for the given numbers.
36, 80, 120

Question 12

Find the greatest common factor of the given terms.
8qr, 28rs, 12qs

Question 13

Factor.
uvw + 9u + 5vw + 45

Question 14

Factor the given polynomial completely. If the polynomial is prime, say so.
n² - 2n

Question 15

Factor.
9z² - 6z + 1

Question 16

Factor the given polynomial completely. If the polynomial is prime, say so.
7w² - 24w - 16

Question 17

Factor.
tu + 5u - 7t - 35

Question 18

Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial.
u³ + 2u² - 11u - 12, u - 3

Question 19

Factor completely.
b³p³ - 6b²p² + 9bp

Question 20

Factor out the greatest common factor.
-63q²r² - 45q²r + 54qr²

Question 21

Factor the given polynomial completely.
z⁶ + 2z³ - 3

Question 22

Solve the given equation.
y² = 9y

Question 23

Audrey uses a slingshot to shoot a marble from a window. The height of the marble h(t) in feet at time t seconds is given by the function h(t) = -16t² - 62t + 188. How many seconds elapse before the marble hits the ground?

Question 24

Solve the equation.

Question 25

Solve the given equation.
x³ + 5x² - 2x - 24 = 0