How do you factor 25r ^ { 2} - 10r - 35?

2 Answers
Mar 26, 2017

5 * ( 5r - 7) * ( r + 1)

Explanation:

You solve it for zero using the discriminant

25r^2 - 10r - 35 = 0

Δ= 10^2 - 4 * 25 * (-35) = 100 + 3500 = 3600

then r1= ( - (-10) + sqrt3600) / ( 2 * 25) = (10 +60 ) / 50 = 7/5

and r2 ( - (-10) - sqrt3600) / ( 2 * 25) = (10 - 60) / 50 = -1

so you use the formula

a * ( r - r1 ) * ( r - r2) and

your answer is ....
25 * ( r - 7/5 ) * (r - (-1) )
or further simplified :

5 * ( 5r - 7) * ( r + 1)

Mar 26, 2017

25r^2-10r-35
=5(5r+7)(r-1)

=25(r+7/5)(r-1)

Explanation:

25r^2-10r-35

=5[5r^2color(blue)(-2r)-7]

=5[5r^2color(blue)(-5r+7r)-7]

=5[color(green)(5r)color(red)((r-1))+color(green)(7)color(red)((r-1))]

=5color(green)((5r+7))color(red)((r-1))

=25(r+7/5)(r-1)