Question

rewrite the following polynomial in standard form.
$10x^2 + 1 - x^3$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. So we need to arrange the terms of \(10x^{2}+1 - x^{3}\) from the highest power of \(x\) to the lowest.

Step2: Identify the exponents of each term

• The term \(-x^{3}\) has an exponent of 3 for \(x\).
• The term \(10x^{2}\) has an exponent of 2 for \(x\).
• The term \(1\) can be thought of as \(1x^{0}\) (since \(x^{0} = 1\)) with an exponent of 0 for \(x\).

Step3: Rearrange the terms

Arrange the terms in descending order of exponents: \(-x^{3}+10x^{2}+1\)

Answer:

\(-x^{3}+10x^{2}+1\)