Question

Factor completely 3x^2+7x-6

Answer 1

I find the following method easiest to factor this equation.

1. First, fill in what you know would be the factors for the first value, 3x^2.  The number 3 only has 2 factors: 3 and 1. Therefore, we know the first values are:

(3x _____)(x_____)

2. Next, figure out what the possible factors for the last value would be (-6). The following combinations are possible:
2 and -3 OR -3 and 2
-2 and 3 OR 3 and -2
-1 and 6  OR 6 and -1
1 and -6 OR -6 and 1

3. Plug in the combinations into step 1 and see which gives you the correct answer:
(3x + 2)(x - 3) = 3x^2 - 7x - 6 --> no
(3x - 3)(x + 2) = 3x^2 + 3x - 6 --> no
(3x - 2)(x + 3) = 3x^2 + 7x - 6 --> YES

Answer 2

$Factor \ 3x^2+7x-6$ 

$1. \ Multiply \ 3 \ by \ -6, \ which \ is \ -18.$

$2. \ Ask: \ Which \ two \ numbers \ add \ up \ to \ 7 \ and \ multiply \ to -18?$

$Answer: \ 9 \ and \ -2$

$4. \ Rewrite \ 7x \ as \ the \ sum \ of \ 9x \ and \ -2x:$

$3x^2+9x-2x-6$ 
 
$3x(x+3)-2(x+3)$  $Factor \ out \ common \ terms \ in \ the \ first \ two \ terms, then \ in \ the \ last$ $two \ terms$ 

$(x+3)(3x-2)$ $Factor \ out \ the \ common \ term \ x+3$