How do you factor $36a^2-3a-5$ ?

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Answer 1 · 2016-05-05T17:13:53

$color(blue)((3a + 1) (12a - 5)$ is the factorised form of the expression.

$36 a^2 - 3a - 5$

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

In this technique, if we have to factorise an expression like $xa^2 + ya + z$ , we need to think of 2 numbers such that:

$N_1*N_2 = x*z = 36 * (-5) = -180$

AND

$N_1 +N_2 = b = -3$

After trying out a few numbers we get $N_1 = -15$ and $N_2 =12$

$12*(-15) = -180$ , and $12+(-15)= -3$

$36 a^2 - 3a - 5= 36 a^2 - 15a + 12a - 5$

$= 3a (12a - 5) + 1 ( 12a - 5)$

$= color(blue)((3a + 1) (12a - 5)$

How do you factor 36a^2-3a-536a^2-3a-5?