1. find the product: (x + 2)( x – 2)

a. x2 − 8
b. 3x2 − 14x − y
c. x2 − 4
d. x2 − 2

2. factor completely: x2 − 36

a. (x + 6)(x – 6)
b. (x + 6)(x + 6)
c. (x – 6)(x − 6)
d. prime

3. factor completely: 4x2 − 81

a. (4x – 9)(x + 9)
b. (2x + 9)(2x + 9)
c. (2x + 9)(2x – 9)
d. (2x – 9)(2x − 9)

4. factor completely: x2 + 16

a. (x + 4)(x + 4)
b. (x + 4)(x – 4)
c. prime
d. (x – 4)(x − 4)

5. factor completely: 2x2 − 18

a. prime
b. 2(x2 − 9)
c. 2(x + 3)(x – 3)
d. 2(x + 3)(x + 3)

6. factor completely: 3x2 − 21

a. 3(x2 − 7)
b. 3(x + 7)(x – 7)
c. 3(x + 7)(x – 3)

Part 1) Option C

Part 2) Option A

Part 3) Option C

Part 4) Option C Prime

Part 5) Option C

Part 6) Option A

Step-by-step explanation:

we know that

A difference of square can be factored in the form

Part 1) Find the product:

Applying difference of square

Part 2) Factor Completely:

Applying difference of square

Part 3) Factor Completely:

Applying difference of square

Part 4) Factor Completely:

Is not a difference of square

Is prime

therefore

Is not possible to factored

Part 5) Factor Completely:

Applying difference of square

Part 6) Factor Completely:

Is not a difference of square

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.