Factor the polynomial f(x)=x4−8x3+128x−256 given that 4 and −4 are zeros.

Question

Factored form: f(x)=

Then identify all real zeros.

If there are multiple zeros, separate the answers with semicolons (;);

x=

Answer 1

know f(x)=(x²-16)*g(x)=x⁴-8x³+128x-256

dividing

g(x)=x²-8x+16=(x-4)²

the root x=4 is a triple root, x=-4 a single root

Answer 2

Use synthetic division/substitution.