Factor completely 3x2 + 9x − 54.

(3x − 9)(x + 6)
3(x − 3)(x + 6)
(3x − 6)(x + 9)
3(x − 2)(x + 9)

Question

Factor completely 3x2 + 9x − 54.

 (3x − 9)(x + 6)
 3(x − 3)(x + 6)
 (3x − 6)(x + 9)
 3(x − 2)(x + 9)

directrix · Answer

For the first step, factor out the common factor of 3.

3^x2 + 9x − 54 = 3* (x^2 + 3x - 18)

directrix · Answer

Focus on factoring: (x^2 + 3x - 18) for now.

directrix · Answer

What are two numbers that multiply to -18 and also add to +3.

We need those to help factor.  @aep0814

anonymous · Answer

-3 and 6

directrix · Answer

Yes.

x^2 + 3x - 18 = x^2 + 6x -3x -18

The +3x has been rewritten as 6x - 3x

directrix · Answer

Factoring by Grouping:

 x^2 + 6x -3x -18 =

x*(x + 6) - 3* (x + 6) =

Note the common factor of (x + 6)
Factor it out 

(x + 6) * (x - 3)

But, that's not the answer.

directrix · Answer

Remember the 3 we factored out at the beginning:

3^x2 + 9x − 54 = 3* (x^2 + 3x - 18)

                           = 3* (x + 6) * (x - 3)

is the complete factorization.   @aep0814

directrix · Answer

Question about this?

anonymous · Answer

No, thank you so much! :)