Question

rewrite the following polynomial in standard form. $x^{2} + 10x^{4} - 6$

Explanation:

Step1: Recall standard form of polynomial

The standard form of a polynomial is written in descending order of the exponents of the variable. That is, the term with the highest degree (exponent) comes first, followed by terms with lower degrees, and then the constant term.

Step2: Identify degrees of each term

• For the term \(10x^{4}\), the degree (exponent of \(x\)) is \(4\).
• For the term \(x^{2}\), the degree is \(2\).
• For the term \(-6\), the degree is \(0\) (since it can be written as \(-6x^{0}\)).

Step3: Arrange terms in descending order

Arrange the terms \(10x^{4}\) (degree 4), \(x^{2}\) (degree 2), and \(-6\) (degree 0) in descending order of their degrees. So the polynomial in standard form is \(10x^{4}+x^{2}-6\).

Answer:

\(10x^{4}+x^{2}-6\)