2 MATH questions can someone HELP PLEASE!!!?

Question

Factor

1. 3x^5 + 15x^3 -108x
2. (x-2)(x^2 -1) -6x - 6


THANKS SO MUCH EVERYONE!!! :)

Answer 1

PROBLEM 1:

First pull out a 3x:
3x(x^4 + 5x² - 36)

Next factor (using y = x²)
3x(x² + 9)(x² - 4)

PROBLEM 2:

Expand the difference of squares:
(x - 2)(x - 1)(x + 1) - 6x - 6

Factor a -6 out of the last part:
(x - 2)(x - 1)(x + 1) - 6(x + 1)

Now factor out the common x + 1:
(x + 1)[(x - 2)(x - 1) - 6]

Expand the stuff in the brackets:
(x + 1)(x² - 3x + 2 - 6)
(x + 1)(x² - 3x - 4)

Then factor:
(x + 1)(x - 4)(x + 1)

So the final factoring is:
(x + 1)²(x - 4)

Answer 2

Divide by x to get x(3x^4 +15x^2-108)
The part inside the bracket is a quadratic.
You want to learn to do quadratic on your own, as they will come back often in your studies (and your work).

Answer 3

1. 3x^5 + 15x^3 -108x
3x(x^4+5x^2-36)
3x(x^2-4)(x^2+9)
3x(x-2)(x+2)(x^2+9)

2. (x-2)(x^2 -1) -6x - 6
(x-2)(x-1)(x+1)-6(x+1)
(x+1)((x-2)(x-1)-6)
(x+1)(x^2-x-2x+2-6)
(x+1)(x^2-3x-6)


x=(1/2)(3+/-√(9+24))
x=(1/2)(3+/-√33)
factors are
(x-3/2-√33 /2)(x-3/2+√33 /2)(x+1)

Answer 4

1. Divide by 3 to get

x^5 + 5x^3 - 36x

Use synthetic division to get the factors:

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

Answer 5

let me do the second one for you
(x-1)(x-1)(x+1)-6(x+1)
=(x+1) [(x-1)(x-1)-6]

Answer 6

18x^8-108x for the 1st one... id give u the 2nd one but i dont paper on me.

Answer 7

theres no equals sign