Notes: How the quadratic may be factored by grouping 5x^2 + 17x

Thursday, December 30, 2010

$\displaystyle{5}{{x}}^{{2}}+{17}{x}-{40}={0}$

$\displaystyle{A}={5}$
$\displaystyle{b}={17}$ $\displaystyle{c}=-{40}$

Multiply $\displaystyle{a}\times{c}$ and find factors of that
number that minus to b

$\displaystyle-{40}\times{5}=-{200}$ factors of -200
that minus to 17 are 25, -8 plug these numbers into the
problem

$\displaystyle{5}{{x}}^{{2}}+{25}{x}-{8}{x}–{40}$ now factor by
grouping

$\displaystyle{\left({5}{{x}}^{{2}}+{25}{x}\right)}{\left(-{8}{x}–{40}\right)}$

Find
the greatest number the numbers in the parenthesis have in common and factor them
out

$\displaystyle{5}{x}{\left({x}+{5}\right)}$
-8(x+5)

(5x-8) (x+5)

and
the answers are (5x-8) (x+5)

Notes