Question

consider the polynomial function
f(x)= x^5+21x^3-100x.
determine the zeros of the function by factoring.

Answer 1

http://www.wolframalpha.com/input/?i=x^5%2B21x^3-100x+determine+the+zeros+of+the+function

Answer 2

because all the terms have an x you can factor that out first:
\[x^5+21x^3-100x = x(x^4+21x^2-100)\]
Then think of two numbers that multiply to -100 but add to 21 (which would be 25 and -4):
\[x(x^4+21x^2-100) = x(x^2+25)(x^2-4)\]
Then factor using a difference of 2 squares:
\[x(x^2+25)(x-2)(x+2)\]