How do you factor $4u^2+9u-28$ ?

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Answer 1 · 2015-05-06T09:43:06

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

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

$N_1*N_2 = a*c = 4*-28 = -112$
AND
$N_1 +N_2 = b = 9$

After trying out a few numbers we get $N_1 = 16$ and $N_2 =-7$

$16*-7 = -112$ , and $16+(-7)= 9$

$4u^2+9u-28 = 4u^2 +16u - 7u -28$

$= 4u(u+4) - 7(u+4)$

$(u+4)$ is a common factor to each of the terms

$=color(green)((u+4)(4u-7)$

How do you factor 4u^2+9u-284u^2+9u-28?