How do you factor the trinomial $x^2-12x+32$ ?

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Answer 1 · 2015-11-23T16:05:58

$color(blue)((x-4)(x-8)$ is the factorised form of the expression.

$x^2-12x+32$

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:

$N_1*N_2 = a*c = 1*32 =32$
AND
$N_1 +N_2 = b = -12$

After trying out a few numbers we get:

$N_1 = -8$ and $N_2 =-4$

$(-8)*(-4) = 32$ , and

$(-8) +(-4)= -12$

$x^2-color(blue)(12x)+32 = x^2color(blue)(-8x-4x)+32$

$=x(x-8) - 4(x-8)$

$(x-8)$ is a common factor to each of the terms.

$color(blue)((x-4)(x-8)$ is the factorised form of the expression.

How do you factor the trinomial x^2-12x+32x^2-12x+32?