How do you factor 2d² +d -21?

Jun 8, 2015

$2 {d}^{2} + d - 21$

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

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

${N}_{1} \cdot {N}_{2} = a \cdot c = 2 \cdot - 21 = - 42$
and
${N}_{1} + {N}_{2} = b = 1$

After trying out a few numbers we get ${N}_{1} = 7$ and ${N}_{2} = - 6$
$7 \cdot - 6 = - 42$, and $7 + \left(- 6\right) = 1$

$2 {d}^{2} + d - 21 = 2 {d}^{2} - 6 d + 7 d - 21$
$= 2 d \left(d - 3\right) + 7 \left(d - 3\right)$
$\left(d - 3\right)$ is common to both terms.

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