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

Question

6276 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-11T16:30:56

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

$2 x^{2} + 13 x - 24$ $2x^2 +13x -24$

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

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

$N_{1} \cdot N_{2} = a \cdot c = 2 \cdot - 24 = - 48$ $N_1*N_2 = a*c = 2*-24 = -48$
and,
$N_{1} + N_{2} = b = 13$ $N_1 +N_2 = b = 13$

After trying out a few numbers we get $N_{1} = 16$ $N_1 = 16$ and $N_{2} = - 3$ $N_2 =-3$

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

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

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

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

How do you factor 2x2+13x−242x^2+13x-24 ?