Is it possible to factor #y=3x^3+4x^2-75x-100 #? If so, what are the factors?

1 Answer
Feb 28, 2016

Answer:

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

Explanation:

group the function into 2 'pairs' as follows.

#[3x^3 + 4x^2 ] + [ -75x - 100 ]#

now factor each pair ( common factor )

1st pair : #x^2(3x+4) #

2nd pair : -25(3x+4)

There is a common factor of (3x+4) in each pair.

hence: (3x+4)(#x^2-25)#

# "now " x^2 - 25 " is a difference of squares "#

which factors as (x-5)(x+5)

#" hence factors are " (3x+4)(x-5)(x+5)#