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

Feb 28, 2016

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

Explanation:

group the function into 2 'pairs' as follows.

$\left[3 {x}^{3} + 4 {x}^{2}\right] + \left[- 75 x - 100\right]$

now factor each pair ( common factor )

1st pair : ${x}^{2} \left(3 x + 4\right)$

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

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

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

$\text{now " x^2 - 25 " is a difference of squares }$

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

$\text{ hence factors are } \left(3 x + 4\right) \left(x - 5\right) \left(x + 5\right)$