How do you factor y= x^2 – 14x – 32?

Mar 21, 2016

 color(blue)((x + 2) ( x -16) is the factorised form of the expression.

Explanation:

$y = {x}^{2} - 14 x - 32$

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:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot \left(- 32\right) = - 32$

AND

${N}_{1} + {N}_{2} = b = - 14$

After trying out a few numbers we get ${N}_{1} = - 16$ and ${N}_{2} = 2$

$\left(- 16\right) \cdot 2 = - 32$ and $2 + \left(- 16\right) = - 14$

${x}^{2} - \textcolor{g r e e n}{14 x} - 32 = {x}^{2} \textcolor{g r e e n}{- 16 x + 2 x} - 32$

$= x \left(x - 16\right) + 2 \left(x - 16\right)$

 = color(blue)((x + 2) ( x -16)

 color(blue)((x + 2) ( x -16) is the factorised form of the expression.