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How do you write $x^{2} - 13 x + 12$ $x^2-13x+12$ in factored form?

1 Answer

Apr 25, 2018

$x^{2} - 13 x + 12 = (x - 1) (x - 12)$ $x^2-13x+12=color(red)((x-1)(x-12))$

Explanation:

Remember
$XXX (x + a) \cdot (x + b)) = x^{2} + (a + b) x + a b$ $color(white)("XXX")(x+color(blue)a) * (x+color(lime)b))=x^2+(color(blue)a+color(lime)b)x+color(blue)acolor(lime)b$

So we are looking for two values, $a$ $color(blue)a$ and $b$ $color(lime)b$ , such that
$XXX a + b = - 13$ $color(white)("XXX")color(blue)a+color(lime)b=-13$
and
$XXX a \cdot b = 12$ $color(white)("XXX")color(blue)a * color(lime)b = 12$

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