# How do you factor 2(x^2) + 9x + 7?

May 13, 2018

$2 \left({x}^{2}\right)$ is just $2 {x}^{2}$
so
$2 {x}^{2} + 9 x + 7$
We know seven is a prime number so its only factors are 7 and 1 therefore we know our final answer will look something like this:
(?x+7)(?x+1)

We also know that 2 is a prime number therefore our x coefficients will be 2 and 1.

we know that $2 x$ x 1 =$2 x$
and $1 x$ x7 = $7 x$
so to get our $9 x$ we can just add $2 x$ and $7 x$

So to times 7 by 1 we put 1 in the opposite bracket, and then do the same for 1 and 2.

$y = 2 {x}^{2} + 9 x + 7$
b. One real roots $x = - \frac{c}{a} = - \frac{7}{2}$ --> factor $\left(x + \frac{7}{2}\right)$
$y = 2 \left(x + \frac{7}{2}\right) \left(x + 1\right) = \left(2 x + 7\right) \left(x + 1\right)$