Factor the polynomial completely. help me please!?

Question

1.64x2 - 81

a(8x + 9)2

b(8x + 9)(8x - 9)

c(8x - 9)2

d prime polynomial

2. (x - 5)2 - y2

a (x - 5 - y)2

b (x - 5 + y)(x + 5 - y)

c (x - 5 + y)(x - 5 - y)

d (x - 5 + y)2

3. 9 - 49x2

a (3 + 7x)(3 - 7x)

b (3 + 7x)2

c (3 - 7x)2

d prime polynomial

4. 21x + 7y - 7

a 7(3x + y - 1)

b 7(3x + y - 7)

c 7x(3 + y)

d 7(3x + y)

5. x3 + 2x + x2 + 2

a (x2 + 1)(2x + 1)

b (x2 + 2)(x + 1)

c (x2 + 1)(x + 2)

d (2x + 1)(x + 1)

6. 3xy - 12x + 7y - 28

a (3x + 7)(y - 4)

b (3x - 4)(y + 7)

c (3x + y)(7y - 4)

d (3x + 7y)(y - 4)

Answer 1

1. The answer is B

Solution: use the principle, a^2 - b^2 = (a+b)(a-b)

64x^2 - 81

= (8x)^2 - 9^2

= (8x + 9)(8x - 9)

2. The answer is C

Solution: use the principle, a^2 - b^2 = (a+b)(a-b)

(x - 5)^2 – y^2

= (x-5 + y)(x-5 – y)

3. The answer is A

9 - 49x^2

= 3^2 – (7x)^2

= (3 + 7x)(3 – 7x)

4. The answer is A

Solution: find the GCF (greatest common factor)

21x + 7y – 7

= 7(3x + y – 1)

5. The answer is B

Solution: find the GCF of the first two terms.

x^3 + 2x + x^2 + 2

= x(x^2 + 2) + x^2 + 2

GCF, again.

x(x^2 + 2) + x^2 + 2

= x(x^2 + 2) + 1(x^2 + 2)

= (x^2 + 2)(x+1)

6. The answer is A

Solution: find the GCF of the first two terms, and then that of the second two.

3xy - 12x + 7y - 28

= 3x(y – 4) + 7(y – 4)

Now there is a common factor, (y-4)

= (y - 4)(3x + 7)

OR (3x + 7)(y – 4)

Answer 2

You're not gonna learn anything by just listing questions and asking for the answers.. the pt is to figure out _how_ to answer one and then practice that approach on the others.

So here is q1:

First off it should be written 64 x^2 so people know it's an exponent.

64x^2 - 81    is aka a difference of squares which have form a^2 - b^2

factored it turns into (a-b)(a+b) therefore:

= (8x)^2 - 9^2

= (8x-9)(8x+9)

good luck though