Determine how many linear factors and zeros each polynomial function has.

$P(x)={x}^{40}+{x}^{39}$

Emeli Hagan
2021-02-27
Answered

Determine how many linear factors and zeros each polynomial function has.

$P(x)={x}^{40}+{x}^{39}$

You can still ask an expert for help

mhalmantus

Answered 2021-02-28
Author has **106** 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$n>0$ and P(x) is an nth-degree polynomial function, then P(x) has exactly n linear factors:

$P(x)={a}_{n}(x-{c}_{1})(X-{c}_{2})(X-{c}_{3}).....(x-{C}_{n})$

Where${c}_{1},{c}_{2},{c}_{3},....,{c}_{n}$ are numbers and ${a}_{n}$ , is the leading coefficient of P(x).

Finding zeros:

Given:

$P(x)={x}^{40}+{x}^{39}$

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$n=40$

Hence the zeros of the polynomial function$P(x)={x}^{40}+{x}^{39}$ is 40

Finding linear factors:

Given:

$P(x)={x}^{40}+{x}^{39}$

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$n=40$

Hence the linear factors of the polynomial function$P(x)={x}^{40}+{x}^{39}$ is 40

Final statement:

The number of linear factors of the polynomial function$P(x)={x}^{40}+{x}^{39}$ are 40.

The zeros of the polynomial function$P(x)={x}^{40}+{x}^{39}$ are 40.

If multiple zeros are counted individually, the polynomial function P(x) with degree

has exactly n zeros among the complex numbers.

The Polynomial Factorization Theorem:

If

Where

Finding zeros:

Given:

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

Hence the zeros of the polynomial function

Finding linear factors:

Given:

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

Hence the linear factors of the polynomial function

Final statement:

The number of linear factors of the polynomial function

The zeros of the polynomial function

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