Question

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)

Answer 1

Part 1) Option C
`x^(2)-4`

Part 2) Option A
`(x+6)(x-6)`

Part 3) Option C
`(2x+9)(2x-9)`

Part 4) Option C Prime

Part 5) Option C
`2(x+3)(x-3)`

Part 6) Option A
`3(x^(2) -7)`

Explanation:

we know that

A difference of square can be factored in the form

`a^(2)-b^(2)=(a+b)(a-b)`

Part 1) Find the product:
`(x + 2)( x - 2)`

Applying difference of square

`(x + 2)( x - 2)=x^(2)-2^(2)`

`(x + 2)( x - 2)=x^(2)-4`

Part 2) Factor Completely:
`x^(2) -36`

Applying difference of square

`x^(2) -36=(x+6)(x-6)`

Part 3) Factor Completely:
`4x^(2) -81`

Applying difference of square

`4x^(2) -81=(2x+9)(2x-9)`

Part 4) Factor Completely:
`x^(2) +16`

Is not a difference of square

Is prime

therefore

Is not possible to factored

Part 5) Factor Completely:
`2x^(2) -18`

`2x^(2) -18=2(x^(2) -9)`

Applying difference of square

`2(x^(2) -9)=2(x+3)(x-3)`

Part 6) Factor Completely:
`3x^(2) -21`

Is not a difference of square

`3x^(2) -21=3(x^(2) -7)`