Finding the solutions

Question

Obtain all the solution(s) of the polynomial equation,

x

4 − 8x

3 + 142 + 8x − 15 , given that x = −1 is a solution

Answer 1

x= 1, -1, 3 and 5

factors are (x-1)(x+1)(x-3)(x-5)

you have a typo in the problem

it should be 14x^2 not 142 for the 3rd term of the polynomial

take x+1, divide it into the given polynomial (corrected on the 3rd term), either by long or synthetic division, to get a cubic. Then try a simple other solution, a simple integer, x=1. Divide the cubic by x-1, to get a quadratic that you can factor. set each factor =0 and get x=3 and x=5