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How do you factor $p^{2} + 12 p + 32$ $p^2 + 12p + 32$ ?

1 Answer

Jun 4, 2015

If $(p^{2} + 12 p + 32)$ $(p^2+12p+32)$
$XXXX$ $color(white)("XXXX")$ has factors $(p + a) (p + b)$ $(p+a)(p+b)$

then we need to find values $a$ $a$ and $b$ $b$ such that
$XXXX$ $color(white)("XXXX")$ $a + b = 12$ $a+b = 12$ and
$XXXX$ $color(white)("XXXX")$ $a \times b = 32$ $axxb= 32$

With a bit of consideration of the possible factors of $32$ $32$
we can come up with $(4, 8)$ $(4,8)$

So
$XXXX$ $color(white)("XXXX")$ $p^{2} + 12 p + 32 = (p + 4) (p + 8)$ $p^2+12p+32 = (p+4)(p+8)$

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