How do you factor $12 x^{2} + 7 x - 5$ $12x^2+7x-5$ ?

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How do you factor $12 x^{2} + 7 x - 5$ $12x^2+7x-5$ ?

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Answer 1 · 2015-09-20T16:52:14

$(12 x - 5) (x + 1)$ $color(blue)((12x-5)(x+1)$ is the factorised form.

Explanation:

$12 x^{2} + 7 x - 5$ $12x^2 +7x -5$

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:

$N_{1} \cdot N_{2} = a \cdot c = 12 \cdot - 5 = - 60$ $N_1*N_2 = a*c = 12*-5 = -60$

and

$N_{1} + N_{2} = b = 7$ $N_1 +N_2 = b = 7$

After trying out a few numbers we get $N_{1} = 12$ $N_1 = 12$ and $N_{2} = - 5$ $N_2 =-5$
$12 \cdot - 5 = - 60$ $12*-5 = -60$ , and $12 + (- 5) = 7$ $12+(-5)= 7$

$12 x^{2} + 7 x - 5 = 12 x^{2} + 12 x - 5 x - 5$ $12x^2 +7x -5 =12x^2 +12x - 5x -5$

$= 12 x (x + 1) - 5 (x + 1)$ $=12x(x+1) -5(x+1)$

$(12 x - 5) (x + 1)$ $color(blue)((12x-5)(x+1)$ is the factorised form.

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How do you factor $12 x^{2} + 7 x - 5$ $12x^2+7x-5$ ?

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How do you factor $12 x^{2} + 7 x - 5$ $12x^2+7x-5$ ?