Determine how many linear factors and zeros each polynomial function has. P(x)=4x^{5}+8x^{3}

Harlen Pritchard 2020-10-28 Answered
Determine how many linear factors and zeros each polynomial function has.
P(x)=4x5+8x3
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Expert Answer

crocolylec
Answered 2020-10-29 Author has 100 answers
Number of zeros theorem:
If multiple zeros are counted individually, the polynomial function P(x) with degree n(n>0) has exactly n zeros among the complex numbers.
The Polynomial Factorization Theorem:
If n>O and P(x) is an nth-degree polynomial function, then P(x) has exactly n linear factors:
P(X)=an(xc1)(xx2)(Xc3)....(xCn)
Where c1,c2,c3,..... Cn are numbers and a_{n}, is the leading coefficient of P(x).
Finding zeros:
Given:
P(x)=4x5+8x3
According to the Number of zeros theorem, the polynomial function P(x) has n zeros.
Where n is the degree of the polynomial function
Here n=5
Hence the zeros of the polynomial function P(x)=4x5+8x3 is 5
Finding linear factors:
Given:
P(x)=4x5+8x3
According to The Polynomial Factorization Theorem, the polynomial function P(x) has n linear factors.
Where n is the degree of the polynomial function
Here n=5
Hence the linear factors of the polynomial function P(x)=4x5+8x3 is 5
Final statement:
The number of linear factors of the polynomial function P(x)=4x5+8x3 are 5.
The zeros of the polynomial function P(x)=4x5+8x3 are 5.
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