How do you factor y=2x^2+11x+12 ?

Aug 2, 2016

$y = \left(2 x + 3\right) \left(x + 4\right)$

Explanation:

Find factors of 2 and 12 which add together to give 11.

find the cross products and add. There is some trial and error.

$\text{ 2 3} \Rightarrow 1 \times 3 = 3$
$\text{ 1 4" rArr 2xx4 = 8 " } 3 + 8 = 11$

The signs are the same they are both positive.

$y = \left(2 x + 3\right) \left(x + 4\right)$

Aug 2, 2016

$\left(x + 4\right) \left(2 x + 3\right)$

Explanation:

First, let's find the zeros of the function y by solving the equation:

$2 {x}^{2} + 11 x + 12 = 0$

$x = \frac{- 11 \pm \sqrt{{11}^{2} - 4 \cdot 2 \cdot 12}}{2 \cdot 2}$

$x = \frac{- 11 \pm \sqrt{121 - 96}}{4}$

$x = \frac{- 11 \pm \sqrt{25}}{4}$

$x = \frac{- 11 \pm 5}{4}$

${x}_{1} = - 4 \mathmr{and} {x}_{2} = - \frac{3}{2}$

You can factor a trynomial:

$y = a {x}^{2} + b x + c = a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$

and have:

$2 {x}^{2} + 11 x + 12 = 2 \left(x + 4\right) \left(x + \frac{3}{2}\right)$

that's

$\left(x + 4\right) \left(2 x + 3\right)$