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

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

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

Vasquez

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:
${x}^{4}-{x}^{3}+{x}^{2}-5$
Result:
yes; ${x}^{4}-{x}^{3}+{x}^{2}-5$

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