Shelia Lawrence

2021-12-30

Is the algebraic expression a polynomial? If it is, write the polynomial in standard form : ${x}^{2}-{x}^{3}+{x}^{4}-5$ .

Jenny Bolton

Beginner2021-12-31Added 32 answers

Step 1

Definition:

The formula for the norm of a polynomial function of degree n is $a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\dots +{a}_{1}x+{a}_{0$ where ${a}_{n}\ne 0$.

Step 2

${x}^{2}-{x}^{3}+{x}^{4}-5$ is the algebraic expression provided.

Yes. The algebraic expression ${x}^{2}-{x}^{3}+{x}^{4}-5$ is a polynomial of degree 4.

Its standard form is ${x}^{4}-{x}^{3}+{x}^{2}-5$.

Anzante2m

Beginner2022-01-01Added 34 answers

This fits the definition of a polynomial. It has multiple terms as well as non-negative integers for exponents. To put it in standard form, we put the exponents in descending order.

Result:

${x}^{4}-{x}^{3}+{x}^{2}-5$

Result:

Vasquez

Expert2022-01-09Added 669 answers

A polynomial is a single term or the sum of two or more terms containing variables with whole-number exponents.

Each term has a variable with whole-number exponent so the algebraic expression is a polynomial. Note that the constant term has a variable with exponent 0.

A polynomial In standard form is written in the order of descending powers of the variable.

So, we rewrite the given as:

Result:

yes;

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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