Determine how many linear factors and zeros each polynomial function has. P(x)=4x5+8x3

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Determine how many linear factors and zeros each polynomial function has.   P(x)=4x5+8x3

crocolylec · Accepted Answer

Number of zeros theorem:  If multiple zeros are counted individually, the polynomial function P(x) with degree n(n&amp;gt;0) has exactly n zeros among the complex numbers.  The Polynomial Factorization Theorem:  If n&amp;gt;O and P(x) is an nth-degree polynomial function, then P(x) has exactly n linear factors:  P(X)=an(x—c1)(x—x2)(X−c3)....(x−Cn)  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.

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

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