2x^2 + 7x^2 -3x -18?

Question

Factor the following polynomial completly, using the fact that x +2 is a factor.

Answer 1

Presumably you meant
2x^3 + 7x^2 - 3x - 18

. . . . 2x^2 + 3x - 9
x + 2)2x^3 + 7x^2 - 3x - 18
. . . .. 2x^3 + 4x^2
. . . . . . . . .. 3x^2 - 3x - 18
. . . . . . . . . . 3x^2 + 6x
. . . . . . . . . . . . . . - 9x - 18
. . . . . . . . . . . . . . - 9x - 18

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

2x^2 + 7x^2 -3x -18 = (x + 2)(2x - 3)(x + 3)

Answer 2

x+2 is not a factor of the above expression. You must have types it wrong. The expresion should be 2x^3 + 7x^2 -3x -18.
Then you divide like doing long division to get

2x^2 + 3x - 9

Answer 3

First off, combine the first two terms 2x^2 + 7x^2 is 9x^2

Now you have a gcf to take out, giving you 3x^2 -x -6
So if one of your factors is (x+2), what does the other one have to be?

You already have the two, so you need a number that multiplies with 2 to get -6 and adds to two to get -1.

Don't forget to put the 3 out front.

Answer 4

(2x³ + 7x² - 3x - 18) / (x + 2) = 2x² + 3x - 9.

Check:
(x + 2)(2x² + 3x - 9) = 2x³ + 3x² - 9x + 4x² + 6x - 18
= 2x³ + 7x² - 3x - 18.

Answer 5

9x^2 - 3x - 18

3 ( x^2 - x - 6 )

3 ( x - 3 )