How do you factor $x^{2} + 4 x - 32$ $x^2+4x - 32$ ?

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How do you factor $x^{2} + 4 x - 32$ $x^2+4x - 32$ ?

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Answer 1 · 2015-05-28T15:06:51

$x^{2} + 4 x - 32$ $x^2+4x - 32$

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:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot (- 32) = - 32$ $N_1*N_2 = a*c = 1*(-32) = -32$
and,
$N_{1} + N_{2} = b = 4$ $N_1 +N_2 = b = 4$
After trying out a few numbers we get $N_{1} = 8$ $N_1 = 8$ and $N_{2} = - 4$ $N_2 =-4$
$8 \cdot (- 4) = - 32$ $8*(-4) = -32$ , and $8 + (- 4) = 4$ $8+(-4)= 4$

$x^{2} + 4 x - 32 = x^{2} + 8 x - 4 x - 32$ $x^2+4x - 32 = x^2+8x - 4x - 32$
$x (x + 8) - 4 (x + 8)$ $x(x+8) -4(x+8)$
$(x - 4) (x + 8)$ $color(green)((x-4)(x+8)$

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How do you factor $x^{2} + 4 x - 32$ $x^2+4x - 32$ ?

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