How do you factor $15 x^{2} + 8 x - 12$ $15x^2 + 8x - 12$ ?

Question

5540 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-22T07:06:19

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:

$N_{1} \cdot N_{2} = a \cdot c = 15 \cdot - 12 = - 180$ $N_1*N_2 = a*c = 15*-12 = -180$
and,
$N_{1} + N_{2} = b = 8$ $N_1 +N_2 = b = 8$

After trying out a few numbers we get:
$N_{1} = - 10$ $N_1 = -10$ and $N_{2} = 18$ $N_2 =18$

$- 10 \cdot 18 = - 180$ $-10*18 = -180$ , and $(- 10) + 18 = 8$ $(-10)+ 18= 8$

$15 x^{2} + 8 x - 12 = 15 x^{2} - 10 x + 18 x - 12$ $15x^2+8x-12 = 15x^2 -10x + 18x -12$

$= 5 x (3 x - 2) + 6 (3 x - 2)$ $= 5x(3x - 2) + 6(3x -2)$

$= (5 x + 6) (3 x - 2)$ $= (5x +6)(3x-2)$ , this is the factorised form.

How do you factor 15x2+8x−1215x^2 + 8x - 12?