Question

I have a test tomorrow and I don't know a single thing. Please, for the love of God, help me. Factor:

1) 125x^3-8 2) 2x^3+54
3) -2X^3-4x^2-3x-6 4) 6x^5-51x^3-27x

Answer 1

1. (5x-2)(25x^2+10x+4)

Answer 2

2. -(x+2)(2x^2+3)

Answer 3

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

Answer 4

1) 125= 5*5*5=5^3; 8=2*2*2
so, 125x^3-8=5^3 *x^3 - 2^3
something like this...?

Answer 5

Well.. because I love God... I will help you.

1) is the difference of 2 cubes.
125x^3 - 8 you need to write each term as ( )^3
(5x)^3 - (2)^3

You have to learn this formula... no other way about it.....
(5x - 2)(25x^2 + 10x + 4) Here is how you get that answer.

Look what is in the ( )'s under the problem (5x) and (2) the first thing you do is
(5x - 2) you put what is in those ( )'s with the sign of the problem.

2nd. You use the (5x) and the (2)
(square the (5x) opposite sign of the problem you take (5x)(2) always a + sign square the(2))
(25x^2 + 10x + 4)

so you have (5x - 2)(25x^2 + 10x + 4)

Answer 6

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

Answer 7

2. 2(x^3 + 27) once again you can write each term as ( )^3
2((x)^3 + (3)^3) so..

we are going to use the (x) and the (3)
(x + 3) (x sign of problem 3)
(x^2 + 3x + 9) (square x, opposite sign of problem (x)(3) always a + square(3))

2(x + 3)(x^2 + 3x + 9)

Answer 8

-2x^3 - 4x^2-3x - 6
first two terms have a greatest common factor of -2x^2
-2x^2(x + 2)

the last two terms have a greatest common factor of -3
-3(x + 2)


so


-2x^2(x + 2) - 3(x + 2)

Both terms have a (x + 2) so you factor it out.

(x + 2)((-2x^2 - 3)

Answer 9

\[4) - 27 x - 51 x^3 + 6 x^5 = (3 (-3 + x) x (3 + x) (1 + 2 x^2)) ?\]

Answer 10

Thank you so far, everyone. I really appreciate your awesome help. :)

Answer 11

what do you need help on