SOLUTION: Factor the polynomial completely. P(x) = 625x4 − 16 Find all its zeros. State the multiplicity of each zero.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the polynomial completely. P(x) = 625x4 − 16 Find all its zeros. State the multiplicity of each zero.      Log On


   

Question 870316: Factor the polynomial completely.
P(x) = 625x4 − 16
Find all its zeros. State the multiplicity of each zero.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
625x%5E4-16=%2825x%5E2-4%29%2825x%5E2%2B4%29=%285x-2%29%285x%2B2%29%2825x%5E2%2B4%29;
The quadratic factor will have two complex zeros, each with imaginary part.
25x%5E2=-4
5%2Ax=-2i and 5x=2i
x=-%282%2F5%29i and x=%282%2F5%29i
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The other zeros, from the linear factors are -%282%2F5%29 and %282%2F5%29.

All multiplicities are 1.