Factor the polynomial P(x)=x4−625, and find all its zeros. State the multiplicity of each zero.
To find the zeros of P, we set x4−625=0, by factoring
x4−625=0(x2−25)(x2+25)=0
Thus, the zeros are x=±5 and x=±5i.
By factorization,
P(x)=(x−5)[x−(−5)](x−5i)[x−(−5i)]=(x−5)(x+5)(x−5i)(x+5i)
We can say that each factors have multiplicity of 1.
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