# How do you write d^2-12d+32 in factored form?

Sep 20, 2015

color(blue)((d-4)(d-8)  is the factorised form of the expression.

#### Explanation:

d^2−12d+32

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 32 = 32$

AND

${N}_{1} + {N}_{2} = b = - 12$

After trying out a few numbers we get ${N}_{1} = - 8$ and ${N}_{2} = - 4$

$\left(- 8\right) \cdot \left(- 4\right) = 32$ and $\left(- 8\right) + \left(- 4\right) = - 12$

d^2−12d+32 = d^2−8d -4d+32

$= d \left(d - 8\right) - 4 \left(d - 8\right)$

color(blue)((d-4)(d-8)  is the factorised form of the expression.