How do you factor $2x^2+13x-24$ ?

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Answer 1 · 2015-08-11T16:30:56

$color(blue)((2x-3)(x+8)$ is the factorised form for the expression.

$2x^2 +13x -24$

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:

$N_1*N_2 = a*c = 2*-24 = -48$
and,
$N_1 +N_2 = b = 13$

After trying out a few numbers we get $N_1 = 16$ and $N_2 =-3$

$16*-3 = -48$ , and $16+(-3)= 13$

$2x^2 +color(blue)(13x) -24 = 2x^2 +color(blue)(16x - 3x) -24$

$= 2x(x+8) - 3(x+8)$

$color(blue)((2x-3)(x+8)$ is the factorised form for the expression.

How do you factor 2x^2+13x-24 2x^2+13x-24 ?