How do you factor 2d² +d -21?

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Answer 1 · 2015-06-08T17:17:38

$2d^2 + d - 21$

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:

$N_1*N_2 = a*c = 2*-21 = -42$
and
$N_1 +N_2 = b = 1$

After trying out a few numbers we get $N_1 = 7$ and $N_2 =-6$
$7*-6 = -42$ , and $7+(-6)= 1$

$2d^2 + d - 21 = 2d^2 - 6d + 7d - 21$
$=2d(d-3)+ 7(d-3)$
$(d-3)$ is common to both terms.

$=color(green)((2d+7)(d-3)$