Question

How do you factor `9x^3-36x^2-25x+100`?

Answer 1

`(x-4)(3x+5)(3x-5)`

Explanation:

There are 4 terms, but there is no common factor in all the terms,
Pair the terms to make common factors, make sure there is a + sign between the pairs.

`9x^3 -36x^2 -25x+100 " = "(9x^3 -36x^2)+ ( -25x+100)`

=`9x^2(x-4) color(magenta)(+) 25(color(blue)(-x+4))`

=`9x^2(x-4) color(magenta)(-) 25(color(blue)(x-4)) larr" "` note sign change.

=`(x-4)(9x^2 -25)`

=`(x-4)(3x+5)(3x-5)`