Question

question
rewrite the following polynomial in standard form.
-3 + 10x³ - 5x²

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written in descending order of the exponents of the variable. For a polynomial in one variable \(x\), the standard form is \(a_nx^n + a_{n - 1}x^{n - 1}+\cdots+a_1x + a_0\), where \(n\) is the highest degree, and \(a_i\) are coefficients.

Step2: Identify the degrees of each term

• For the term \(-3\), the degree of \(x\) is \(0\) (since \(-3=-3x^0\)).
• For the term \(10x^3\), the degree of \(x\) is \(3\).
• For the term \(-5x^2\), the degree of \(x\) is \(2\).

Step3: Rearrange the terms in descending order of degrees

The highest degree term is \(10x^3\) (degree 3), then \(-5x^2\) (degree 2), then \(-3\) (degree 0). So we rearrange the polynomial \(-3 + 10x^3-5x^2\) to \(10x^3-5x^2 - 3\).

Answer:

\(10x^3 - 5x^2 - 3\)