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How do you factor $14 x^{2} + 29 x - 15$ $14x^2 + 29x - 15$ ?

1 Answer

May 29, 2015

If $14 x^{2} + 29 x - 15$ $14x^2+29x-15$
$= (a x + b) (c x - d) XXXXX$ $=(ax+b)(cx-d) color(white)("XXXXX")$ we know there needs to be a 'minus' on the $d$ $d$ because of the 'minus' on $15$ $15$

then we are looking for

factors $a and c$ $a and c$ of $14$ $14$ , and
factors $b and d$ $b and d$ of $15$ $15$
such that $b c - a d = 29$ $bc-ad = 29$

Fortunately there are not a lot of factor pairs for $14 and 15$ $14 and 15$
so we can quickly come up with
$(2 x + 5) (7 x - 3)$ $(2x+5)(7x-3)$

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