How do you factor $8 u^{2} + 6 u - 9$ $8u^2 + 6u - 9$ ?

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How do you factor $8 u^{2} + 6 u - 9$ $8u^2 + 6u - 9$ ?

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Answer 1 · 2015-06-16T22:42:02

$8 u^{2} + 6 u - 9 = (2 u + 3) (4 u - 3)$ $8u^2+6u-9 = (2u+3)(4u-3)$

Explanation:

We need to look at factors of
$XXXX$ $color(white)("XXXX")$ $8$ $8$
$XXXX$ $color(white)("XXXX")$ $(a, b) ε {(1, 8), (2, 4)}$ $(a,b) epsilon {(1,8), (2,4)}$
and
$XXXX$ $color(white)("XXXX")$ $(- 9)$ $(-9)$
$XXXX$ $color(white)("XXXX")$ $(c, d) ε {(1, - 9), (- 1, 9), (3, - 3), (- 3, 3)}$ $(c,d) epsilon {(1,-9), (-1,9), (3,-3), (-3,3)}$

such that
$XXXX$ $color(white)("XXXX")$ $a c - b d = + 6$ $ac - bd = +6$

then plug them into
$XXXX$ $color(white)("XXXX")$ $(a u + c) (b u + d)$ $(au+c)(bu+d)$

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How do you factor $8 u^{2} + 6 u - 9$ $8u^2 + 6u - 9$ ?

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