Determine how many linear factors and zeros each polynomial function has. P(x)=x40+x39

Question

Determine how many linear factors and zeros each polynomial function has.   P(x)=x40+x39

mhalmantus · Accepted Answer

Amount of zeros theorem: The degree three polynomial function P(x) holds true if numerous zeros are counted independently&amp;nbsp;n(n&amp;gt;0)&amp;nbsp;has exactly n zeros among the complex numbers.&amp;nbsp;The Polynomial Factorization Theorem:&amp;nbsp;If&amp;nbsp;n&amp;gt;0&amp;nbsp;if P(x) has exactly n linear elements and P(x) is a polynomial function of the nth degree:P(x)=an(x−c1)(X−c2)(X−c3).....(x−Cn)&amp;nbsp;Where&amp;nbsp;c1,c2,c3,....,cn&amp;nbsp;are numbers and&amp;nbsp;an, is the leading coefficient of P(x).&amp;nbsp;Finding zeros:&amp;nbsp;Given:&amp;nbsp;P(x)=x40+x39&amp;nbsp;The polynomial function P(x) has n zeros, according to the Number of Zeros Theorem.where n is the polynomial function&#039;s degreeHere&amp;nbsp;n=40&amp;nbsp;Hence the zeros of the polynomial function&amp;nbsp;P(x)=x40+x39&amp;nbsp;is 40&amp;nbsp;Finding linear factors:&amp;nbsp;Given:&amp;nbsp;P(x)=x40+x39&amp;nbsp;The polynomial function P(x) has n linear factors, according to The Polynomial Factorization Theorem.where n is the polynomial function&#039;s degreeHere&amp;nbsp;n=40&amp;nbsp;Hence the linear factors of the polynomial function&amp;nbsp;P(x)=x40+x39&amp;nbsp;is 40&amp;nbsp;The polynomial function&#039;s number of linear elements is the conclusion.P(x)=x40+x39&amp;nbsp;are 40.&amp;nbsp;The zeros of the polynomial function&amp;nbsp;P(x)=x40+x39&amp;nbsp;are 40.

Determine how many linear factors and zeros each polynomial function has. P(x)=x^{40} + x^{39}

Answered question

Answer & Explanation

New Questions in Algebra II