How do you write 3y²-16y-12 in factored form?

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Answer 1 · 2015-09-19T15:33:06

$color(green)((3y+2) (y -6)$ is the factorised form.

$3y^2-16y-12$

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

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

$N_1*N_2 = a*c = 3*-12 = -36$
and
$N_1 +N_2 = b = -16$

After trying out a few numbers we get $N_1 = -18$ and $N_2 =2$
$-18*2 = -36$ , and $-18+(2)= -16$

$3y^2-16y-12 =3y^2-18y +2y-12$

$= 3y(y -6) +2 (y-6)$

$color(green)((3y+2) (y -6)$ is the factorised form.