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

Answer:

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 $3(x^{2} -7)$

Step-by-step 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

$3x^{2} -21=3(x^{2} -7)$