How do you write $d^2-18d+80$ in factored form?

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Answer 1 · 2015-09-16T15:57:01

$color(blue)((d-8)(d-10)$ is the factorised form of the expression.

$d^2 -18d +80$

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

In this technique, if we have to factorise an expression like $ad^2 + bd + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 1*80 = 80$
and
$N_1 +N_2 = b = -18$

After trying out a few numbers we get $N_1 = -10$ and $N_2 =-8$
$-10*-8 = 80$ , and $(-10)+(-8)= -18$

$d^2 -18d +80= d^2 -10d-8d +80$

$=d(d-10) -8(d -10)$

$=color(blue)((d-8)(d-10)$

How do you write d^2-18d+80d^2-18d+80 in factored form?