Question

X^3 + 5x^2 - 8x^2 - 40x + 7x + 35

Answer 1

Remark

x - 1 is a root.

Proof

x - 1 = 0

x =  1

(1)^3 + 5(1)^2 - 8(1)^2 - 40(1) + 7(1) + 35

1 + 5 - 8 - 40 + 7 + 35

6 + 7 + 35 - 48 = 0

Solution

Divide x - 1 into the original equation.

x^3 + 5x^2 - 8x^2 - 33x + 35

x - 1 || x^3 - 3x^2  - 33x + 35  || x^2 - 2x  - 35

         x^3 -  x^2

                  -2x^2 - 33x

                   -2x^2 + 2x

                             - 35x + 35

                             -35x + 35

                                       0

x^2 - 2x - 35 factors into (x - 7)(x + 5)

Complete factorization

(x - 1)(x - 7)(x + 5)