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How do you factor $x^{2} + 8 x + 12$ $x^2 + 8x + 12$ ?

1 Answer

Jun 12, 2016

$x^{2} + 8 x + 12 = (x + 2) (x + 6)$ $x^2+8x+12=color(green)((x+2)(x+6))$

Explanation:

In general
$XXX (x^{2} + (a + b) x + a \cdot b) = (x + a) (x + b)$ $color(white)("XXX")(x^2+(color(red)(a)+color(blue)(b))x+color(red)(a)*color(blue)(b))=(x+color(red)(a))(x+color(blue)(b))$

$8 = 2 + 6$ $8 = color(red)(2)+color(blue)(6)$
and
$12 = 2 \cdot 6$ $12=color(red)(2)*color(blue)(6)$

So
$x^{2} + 8 x + 12$ $x^2+8x+12$

$XXX = (x^{2} + (2 + 6) x + 2 \cdot 6$ $color(white)("XXX")=(x^2+(color(red)(2)+color(blue)(6))x+color(red)(2)*color(blue)(6)$

$XXX = (x + 2) (x + 6)$ $color(white)("XXX")=(x+color(red)(2))(x+color(blue)(6))$

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