Complete Factorization Factor the polynomial completely, and find all its zeros.State the multiplicity of each zero. P(x) = x^{5}+7x^{3}

Ernstfalld 2020-11-30 Answered
Complete Factorization Factor the polynomial completely, and find all its zeros.State the multiplicity of each zero.
P(x)=x5+7x3
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Expert Answer

broliY
Answered 2020-12-01 Author has 97 answers
Concept used:
The multiplicity of zero of the polynomial having factor (xc) that appears k times in the factorization of the polynomial is k.
Calculation:
The given polynomial is P(x)=x5+7x3.
Factor the above polynomial to obtain the zeros.
P(x)=x5+7x3
=x3(x2+7)
=x3(x2(7i)2)
=x3(x7i)(x+7i)
Substitute 0 for P (x) in the polynomial P(x)=x5+7x3 to obtain the zeros of the polynomial
. x3(x7i)(x+7i)
Further solve for the value of x as,
x3=0,(x7i)=0 and (x+7i)=0
x=0,x=7i and x=7i
The zeros of the polynomial P(x)=x5+7x3 appears three times and one time in the polynomial therefore, the multiplicity of the zero 0 is 3, 7i and 7i is 1.
Conclusion:
Thus, the factorization of the polynomial P(x)=x5+7x3 is P(x)=x3(x7i)(x+7i), zeros of the polynomial are 0 and + 7i and the multiplicity of the zero 0 is 3, 7i and 7i is 1.
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