Math factor please help?

Question

Could anyone please help me with these math problems?? Thank so much

1. The GCF of the binomial 12x^3y - 8x^2 y^2 is ?

A) 2xy
B) 4xy^2
C) 8x^2 y^2
D) 4x^2y

2. Factor completely 4x^2 - 9
A) (2x + 3)(2x + 3)
B) (2x + 3)(2x - 3)
C) (2x-3)^2
D) (4x + 3)(x - 3)

3. Factor completely p^4 - 81
A) (p^2+9)(p^2 - 9)
B) (p+3)^2(p-3)^2
C) (p-9)^2
D) (p^2+9)(p+3)(p-3)

Answer 1

(1) The GCF of 12 and 8 is 4, and for the variables, you use the lower degree. So the answer to #1 is 4x^2y {D}

(2) This is a difference of two squares, which easily factors into (2x-3)(2x+3) {B}

(3) This is also a difference of two squares, but twice:

(p^2 - 9)(p^2 + 9)
(p-3)(p+3)(p^2+9) {D}

Notice the SUM of 2 squares doesn't factor

Answer 2

#1--The greatest common thing that can be factored out of the binomial is D.

Well, #2 is the difference of two squares. The answer is B.

#3, also the difference of two squares. First it is (p^2 + 9) (p^2 - 9), but then notice that (p^2 - 9) is also the difference of two squares. In order to factor completely, this has to be broken down into (p + 3) (p - 3). The answer is D.

Answer 3

1. The GCF of the binomial 12x^3y - 8x^2 y^2 is ?
D) 4x^2y

2. Factor completely 4x^2 - 9
B) (2x + 3)(2x - 3)


3. Factor completely p^4 - 81
A) (p^2+9)(p^2 - 9)

Answer 4

1. D.4x^2y
2. (2x+3)(2x-3)

3. (p^2+9)(p^2-9)
(p^2+9)(p+3)(p-3)

Answer 5

6x2 - 13x - 5 = 6x2 + 2x - 15x - 5 = 2x(3x + 1) - 5(3x + 1) = (3x + 1) (2x - 5)

Answer 6

1. B
2. C
3. A

Answer 7

1) D
2) B
3) A

Answer 8

sorry, only in pre-algebra! wish i could help! best of luck!