How do you factor the trinomial $3m ^2 + 8m -3$ ?

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Answer 1 · 2016-04-06T12:50:27

$color(purple)((3m - 1) ( m + 3 )$ is the factorised form of the expression.

$3m^2 + 8m - 3$

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

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

$N_1*N_2 = a*c = 3*(-3) = -9$

AND

$N_1 +N_2 = b = 8$

After trying out a few numbers we get $N_1 = 9$ and $N_2 =-1$
$9*(-1) = -9$ , and $9+(-1)= 8$

$3m^2 + 8m - 3 =3m^2 + 9m - 1m - 3$

$=3m ( m + 3 ) - 1 ( m + 3 )$

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

$color(purple)((3m - 1) ( m + 3 )$ is the factorised form of the expression.

How do you factor the trinomial 3m ^2 + 8m -33m ^2 + 8m -3?