Factor by grouping.

Question

Factor by grouping.

yanasidlinskiy · Answer

$$3x^2+7x$$

yanasidlinskiy · Answer

I need the steps to the final answer.

yanasidlinskiy · Answer

Ther's a -6 at the end.

hartnn · Answer

$ 3x^2+7x-6 $

can you tell me 2 numbers whose sum is +7 and product is 3*6 = 18 ?

hartnn · Answer

***
can you tell me 2 numbers whose sum is +7 and product is 3*(-6) = -18 ?

yanasidlinskiy · Answer

it would be  3 and 4????? idk.never learned this.

hartnn · Answer

what are factors of 18 ?

yanasidlinskiy · Answer

1,2,3,6,9,18

hartnn · Answer

so we need the sum as +7

how about taking 9 and -2 ??

sum = +7 and product = 9*-2 = -18 !
got how to find such 2 numbers here ?

hartnn · Answer

so we split +7x as $\large +9x-2x$

$\large 3x^2+9x-2x-6$

try to factor out +3x from first 2 terms, what u get ?

yanasidlinskiy · Answer

How would I do that??

hartnn · Answer

$\Large 3x(x+3) -2 (x+3)$

here, i also factored -2 from last 2 terms.....did u get this step ?

yanasidlinskiy · Answer

OMG...you are so smart!!...yes i got this step!

hartnn · Answer

now we can factor out (x+3) entirely.
$\large (x+3) [3x -2]$

so your final factored form will be 
$\Large (x+3)(3x-2)$
thats it!

yanasidlinskiy · Answer

Thank you so much!!!! Your're the the best!!!!!

hartnn · Answer

You're welcome ^_^