How do you factor 3x^2 + 13x - 10  by grouping?

Aug 31, 2016

$3 {x}^{2} + 13 x - 10 = \left(3 x - 2\right) \left(x + 5\right)$

Explanation:

Let the quadratic polynomial to be factorized be $a {x}^{2} + b x + c$. To factorize using grouping method, one needs to split middle term $b$ in two parts, so that their sum is $b$ and product is a×c.

In $3 {x}^{2} + 13 x - 10$, we should split $13$ in two parts so that their product is 3×(-10)=-30. Sich numbers are $15$ and $- 2$ and hence

$3 {x}^{2} + 13 x - 10$

= $3 {x}^{2} + 15 x - 2 x - 10$

= $3 x \left(x + 5\right) - 2 \left(x + 5\right)$

= $\left(3 x - 2\right) \left(x + 5\right)$