How do you factor $12x^2-4x-40$ ?

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Answer 1 · 2016-05-01T16:55:28

$color(blue)((12x + 20 ) (x-2)$ is the factorised form of the expression.

$12x^2 - 4x - 40$

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:

$N_1*N_2 = a*c = 12*(-40) = -480$

AND

$N_1 +N_2 = b = -4$

After trying out a few numbers we get $N_1 = 20$ and $N_2 =-24$
$20 *(- 24) = - 480$ , and $20+(-24)= -4$

$12x^2 - 4x - 40 = 12x^2 - 24 x + 20x - 40$

$= 12x(x-2) + 20 ( x-2)$

$(x-2)$ is a common factor to each of the terms
$color(blue)((12x + 20 ) (x-2)$ is the factorised form of the expression.

How do you factor 12x^2-4x-4012x^2-4x-40?