Question

Can someone help me factor 2b^2+3b-2?
It's been awhile sinece I last factored.

Answer 1

(b+2)(2b−1)

Answer 2

thank you!

Answer 3

Yes, here's how to do it:

\[2b^2+3b-2\]

Multiply the coefficients of the first and last terms:

2*(-2) = -4

Now, factor -4 and look for a pair of factors which adds to 3:

-1*4 = -4, and -1 + 4 = 3, so that's our pair.

Rewrite the original polynomial, splitting the middle term with those factors:
\[2b^2- 1b + 4b -2\]Group each pair of terms:
\[(2b^2-1b) + (4b-2)\]Factor each group
\[b(2b-1) + 2(2b-1)\]Notice that \((2b-1)\) is a common factor to both, and factor it out:
\[(2b-1)(b+2)\]

Check by multiplication:
\[(2b-1)(b+2) = 2b(b+2) - 1(b+2) = 2b^2 + 4b -1b -2 = 2b^2 +3b -2 \checkmark\]