How do you factor the trinomial $12m^2+20m+3$ ?

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Answer 1 · 2015-12-07T12:44:46

$12m^2+20m+3 = color(green)((2m+3)(6m+1)$

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

In this technique, if we have to factorize an expression like $am^2 + bm + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 12*3 = 36$

and

$N_1 +N_2 = b = 20$

After trying out a few numbers we get $N_1 = 18$ and $N_2 =2$
$18*2 = 36$ , and $18+2= 20$

$12m^2+20m+3 = 12m^2 +18m + 2m + 3$

$= 6m(2m + 3) + 1(2m + 3)$

$(2m+3)$ is a common factor to each of the terms

$=color(green)((2m+3)(6m+1)$

How do you factor the trinomial 12m^2+20m+312m^2+20m+3?