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

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

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Answer 1 · 2015-09-19T15:33:06

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

Explanation:

$3 y^{2} - 16 y - 12$ $3y^2-16y-12$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot - 12 = - 36$ $N_1*N_2 = a*c = 3*-12 = -36$
and
$N_{1} + N_{2} = b = - 16$ $N_1 +N_2 = b = -16$

After trying out a few numbers we get $N_{1} = - 18$ $N_1 = -18$ and $N_{2} = 2$ $N_2 =2$
$- 18 \cdot 2 = - 36$ $-18*2 = -36$ , and $- 18 + (2) = - 16$ $-18+(2)= -16$

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

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

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

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

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