# How do you factor 7x^2 + 51x + 14?

Mar 14, 2016

$\left(7 x + 2\right) \left(x + 7\right)$ is the factorised form of the expression.

#### Explanation:

$7 {x}^{2} + 51 x + 14$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 7 \cdot 14 = 98$

AND

${N}_{1} + {N}_{2} = b = 51$

After trying out a few numbers we get ${N}_{1} = 49$ and ${N}_{2} = 2$

$49 \cdot 2 = 98$, and $49 + 2 = 51$

$7 {x}^{2} + 51 x + 14 = 7 {x}^{2} + 49 x + 2 x + 14$

$= 7 x \left(x + 7\right) + 2 \left(x + 7\right)$

$= \left(7 x + 2\right) \left(x + 7\right)$

$\left(7 x + 2\right) \left(x + 7\right)$ is the factorised form of the expression.