Monday, August 31, 2015

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 24

Factor the polynomial P(x)=x4625, and find all its zeros. State the multiplicity of each zero.

To find the zeros of P, we set x4625=0, by factoring


x4625=0(x225)(x2+25)=0


Thus, the zeros are x=±5 and x=±5i.

By factorization,


P(x)=(x5)[x(5)](x5i)[x(5i)]=(x5)(x+5)(x5i)(x+5i)


We can say that each factors have multiplicity of 1.

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