How do I factor 12b^2 + 25b - 7 ?
I've completely forgotten what I'm supposed to do and my book isn't particularly helping.

Question

How do I factor 12b^2 + 25b - 7 ? 
I've completely forgotten what I'm supposed to do and my book isn't particularly helping.

whpalmer4 · Answer

multiply 12 and -7, what do you get?

anonymous · Answer

-84 ?

whpalmer4 · Answer

yes. now, what are two factors of -84 that add to 25?

anonymous · Answer

-3 and 28 ?

rhondasommer · Answer

Multiply 12 by -7, which is -84.
Which two numbers add up to 25 and multiply to -84?
 28 and -3
Rewrite 25b as the sum of 28b and −3b

whpalmer4 · Answer

yes.  this means we can split the 25b term into -3b and 28 b:
$$12b^2+28b-3b-7$$
now we need to take a pair of those terms so that we can factor it.

can't factor $3b-7$ so we will do $28b-7$ which we can factor as $$7(4b-1)$$
how about the other two terms?

rhondasommer · Answer

no because you are suppposed to divide the largest number possible being 4b

whpalmer4 · Answer

$$12b^2-3b=3b(4b-1)$$
notice that the bit in the ( ) is identical to that in our other term?

$$12b^2+28b-3b-7= (12b^2-3b) + (28b-7) = 3b(4b-1)+7(4b-1)$$$$=(3b+7)(4b-1)$$

anonymous · Answer

So from 12b^2+28b−3b−7 I can factor by grouping and get 3b(4b-1) + 7(4b-1) which is the same as (3b+7)(4b-1) right? And that'd be the answer?

whpalmer4 · Answer

checking our work: $$(3b+7)(4b-1)=(3b)(4b)+(-1)(3b)+7(4b)+7(-1)=12b^2+28b-3b-7$$$$=12b^+25b-7\checkmark$$

whpalmer4 · Answer

yes, mangled the formatting a bit on my last post, but your answer is correct

anonymous · Answer

Okay ! Thank you a ton, I forgot what to do and I was super confused. I think i get it now though. Again, thanks !

whpalmer4 · Answer

I always have to figure it out again when I haven't done it for a while!