How do you factor $2x^2-5x-12$ ?

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Answer 1 · 2015-08-05T13:52:14

$=color(green)((2x+3)(x-4)$

$2x^2−5x−12$

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

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

$N_1*N_2 = a*c = 2*-12 = -24$
and,
$N_1 +N_2 = b = -5$

After trying out a few numbers we get:
$N_1 = -8$ and $N_2 =3$
$3*(-8) = -24$ , and
$3+(-8)= -5$

$2x^2−color(blue)(5x)−12 = 2x^2−color(blue)(8x +3x)−12$

$= 2x(x-4) +3(x-4)$

$(x-4)$ is a common factor to each of the terms

$=color(green)((2x+3)(x-4)$

How do you factor 2x^2-5x-12 2x^2-5x-12 ?