Question

Determine which of the following numbers is not a root of

f(x)=x^5-5x^4-17x³+85x² +16x-80.

Answer choices:
1. 5
2. -4
3. -5
4. 4

Answer 1

-5

Explanation:

Simplify f(x)

`f(x)=x^5-5x^4-17x^3+85x^2+16x-80\\f(x)=x^4(x-5)-17x^2(x-5)+16(x-5)\\f(x)=(x^4-17x^2+16)(x-5)\\f(x)=(x^2-16)(x^2-1)(x-5)\\f(x)=(x-4)(x+4)(x+1)(x-1)(x-5)`

Therefore,
`x=4,-4,-1,1,5` are the roots of the polynomial
`f(x)`, which makes option 3 the best choice.