How do you factor the trinomial $3 x^{2} + 2 x - 1 = 0$ $3x^2+2x-1=0$ ?

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How do you factor the trinomial $3 x^{2} + 2 x - 1 = 0$ $3x^2+2x-1=0$ ?

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Answer 1 · 2016-03-01T18:35:58

$(3 x - 1) (x + 1)$ $(3x-1) (x+1)$ is the factorised form of the expression.

Explanation:

$3 x^{2} + 2 x - 1 = 0$ $3x^2 + 2x- 1 =0$

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

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 3 \cdot - 1 = - 3$ $N_1*N_2 = a*c = 3*-1 = -3$

AND

$N_{1} + N_{2} = b = 2$ $N_1 +N_2 = b = 2$

After trying out a few numbers we get $N_{1} = - 1$ $N_1 = -1$ and $N_{2} = 3$ $N_2 =3$
$3 \cdot - 1 = - 3$ $3*-1 = -3$ , and $3 + (- 1) = 2$ $3+(-1)= 2$

$3 x^{2} + 2 x - 1 = 3 x^{2} + 3 x - 1 x - 1$ $3x^2 + 2x- 1 =3x^2 + 3x -1x- 1$

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

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

$(3 x - 1) (x + 1)$ $(3x-1) (x+1)$ is the factorised form of the expression.

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How do you factor the trinomial $3 x^{2} + 2 x - 1 = 0$ $3x^2+2x-1=0$ ?

1 Answer

Explanation:

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How do you factor the trinomial $3 x^{2} + 2 x - 1 = 0$ $3x^2+2x-1=0$ ?