Quadratic Factoring

Question

5x² -9x -18

5x² + 6x -15x -18

x(5x+6) -3(5x-6)

 

I know the answer is (x-3)(5x+6). My question is, how do you determine whether to use (5x+6) or (5x-6)?

Answer 1

We can use the AC method.  Find multiply 5 by -18.  Then find two integers that multiply to the product and add to the middle coefficient.

 

5 * -18 = -90

 

____ * ____ = -90

 

____ + ____ = -9

 

 

6 and -15 work out perfectly.

 

5x² - 15x + 6x - 18 =

 

5x(x - 3) + 6(x - 3) =

 

(x - 3)(5x + 6)

 

 

FYI, you made an error in signs in your work.  It should    x(5x + 6) - 3(5x + 6).  Then you would get the same result I got.

Answer 2

Ah, when you factor the -3 out of -15x-18, it becomes -3(5x+6).  Remember taking -3 out of -18, you get (-3)·(+6) = -18.

Answer 3

5x² -9x -18
5x² + 6x -15x -18
x(5x+6) -3(5x-6)   <-- in this step where you factored out -3, the parentheses should be (5x + 6) because -18/-3 = +6

 

Then you can see that you factor out the common factor of (5x + 6)!