Help. ​

1.   4x³ + 8x² - 96x

                                      Factor  4x  out of each term.

=    4x(x² + 2x - 24)

                                      Factor  x² + 2x - 24  as  (x - 4)(x + 6) .

=  4x(x - 4)(x + 6)

(The one you have selected is right.    )

3.     We want to solve this equation for  x :

0  =  x⁴ - 4x³ + 3x²

                                      Factor  x²  out of all the terms on the right side.

0  =  x²(x² - 4x + 3)

                                      Factor  x² - 4x + 3  as  (x - 1)(x - 3) .

0  =  x²(x - 1)(x - 3)

                                      And we can "factor"  x²  as  x * x .

0  =  (x)(x)(x - 1)(x - 3)

                                      Set each factor equal to zero and solve for  x .

x  =  0       or       x  =  0       or       x  =  1       or       x  =  3

x  =  0  occurs twice, so it has multiplicity  2 .

x  =  1  occurs once, so it has multiplicity  1 .

x  =  3  occurs once, so it has multiplicity  1 .