How do you factor completely: $3x^2 + 2x − 1$ ?

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Answer 1 · 2015-07-24T13:34:10

$=color(blue)((3x-1)(x+1)$

$3x^2+2x−1$

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:

$N_1*N_2 = a*c = 3*-1 = -3$
and
$N_1 +N_2 = b = 2$

After trying out a few numbers we get:
$N_1 = 3$ and $N_2 =-1$
$3*(-1) = -3$ , and $3+(-1)=2$

$3x^2+2x−1 =3x^2+3x -1x−1$

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

$(x+1)$ is common to both terms here:

$=color(blue)((3x-1)(x+1)$

How do you factor completely: 3x^2 + 2x − 13x^2 + 2x − 1?