How do you factor 2x^2+19x+24?

Jan 27, 2018

$\left(2 x + 3\right) \left(x + 8\right)$

Explanation:

When you factor a quadratic equation of the form $a {x}^{2} + b x + c$, you must find two numbers which, when multiplied, give $a c$, and when added, give $b$.

First let us compute $a c$.
$2 \cdot 24 = 48$

Therefore, the two numbers add up to $19$, and multiply to give $48$.

List out the factors of $48$. I'm going to list them in pairs (each pair will multiply to give $48$, for example, $4$ and $12$). You should be able to run through the factors in your head; listing out takes a lot of time.

$\left(1 , 48\right) , \left(2 , 24\right) , \left(3 , 16\right) , \left(4 , 12\right) , \left(6 , 8\right)$.

Now, what of the above pairs add up to $19$? $3$ and $16$ do.

So now we have the equation, $2 {x}^{2} + 19 x + 24$

$= 2 {x}^{2} + 16 x + 3 x + 24$ (the factor pair)

$= 2 x \left(x + 8\right) + 3 \left(x + 8\right)$

$= \left(2 x + 3\right) \left(x + 8\right)$

Factored.