SOLUTION: Write the polynomial as the product of linear factors. List all the zeroes of the function as well. f(x) = x4 − 81 Thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write the polynomial as the product of linear factors. List all the zeroes of the function as well. f(x) = x4 − 81 Thank you!      Log On


   

Question 995742: Write the polynomial as the product of linear factors. List all the zeroes of the function as well.
f(x) = x4 − 81

Thank you!
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the polynomial as the product of linear factors. List all the zeroes of the function as well.
f(x) = x4 − 81
-----------------------------------------------------------------------

f(x) = x%5E4-81 = %28x%5E2-9%29%2A%28x%5E2%2B9%29 = %28x-3%29%2A%28x%2B3%29%2A%28x-3i%29%2A%28x%2B3i%29

is factorization of the polynomial into the product of linear factors.
Notice that the two last factors include complex numbers.

The roots of the polynomial are -3, 3, -3i and 3i.