Question

what are the bionomial factors of the polynomial x^3-5x^2+2x+8

Answer 1

`(x+1)(x-2)(x-4)`

Explanation:

By the Rational Root Theorem, possible rational solutions for the given polynomial are
`\pm1,\pm2,\pm4,\text{ and}\pm8`, so we can test each one:

1 | 1 -5 2 8

____ 1_-4_-2

1 -4 -2 | 6 <-- (x-1) IS NOT a root

-1 | 1 -5 2 8

____-1_ 6_ -8

1 -6 8 | 0 <-- (x+1) IS a root

So,
`x^3-5x^2+2x+8=(x+1)(x^2-6x+8)=(x+1)(x-2)(x-4)`