Emeli Hagan

2021-02-27

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

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

mhalmantus

Skilled2021-02-28Added 105 answers

Amount of zeros theorem: The degree three polynomial function P(x) holds true if numerous zeros are counted independently $n(n>0)$ has exactly n zeros among the complex numbers.

The Polynomial Factorization Theorem:

If $n>0$ if P(x) has exactly n linear elements and P(x) is a polynomial function of the nth degree:

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

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

Finding zeros:

Given:

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

The polynomial function P(x) has n zeros, according to the Number of Zeros Theorem.

where n is the polynomial function's degree

Here $n=40$

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

Finding linear factors:

Given:

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

The polynomial function P(x) has n linear factors, according to The Polynomial Factorization Theorem.

where n is the polynomial function's degree

Here $n=40$

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

The polynomial function's number of linear elements is the conclusion.

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

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

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