Question

Can someone help me rewrite this polynomial into a standard form

Answer 1

x³ + 10x² + 1

Explanation:

To rewrite the given polynomial in standard form, we need to arrange the terms in descending order of the exponent of the variable. The standard form of a polynomial is the form where the terms are written from highest to lowest degree.

The given polynomial is:

10x² + 1 - x³

To rewrite it in standard form, we first rearrange the terms in descending order of the exponent:

∴ x³ + 10x² + 1

Now the polynomial is in standard form.
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Additional Information:

Polynomial: A polynomial is a mathematical expression that consists of variables (like x), coefficients (numbers), and non-negative integer exponents. The standard form of a polynomial is written with the terms in descending order of the exponents.

Degree of a polynomial: The degree of a polynomial is the highest exponent of the variable in that polynomial. In the given polynomial, the term with the highest degree is -x^3, so the degree of the polynomial is 3.

Exponent: The exponent of a term indicates the number of times the variable is multiplied by itself. For example, x^3 means x · x · x.

Coefficient: The coefficient is the number that multiplies the variable in each term. For example, in the term 10x^2, the coefficient is 10.

Descending order: When arranging the terms of a polynomial in descending order, we write the term with the highest degree first, followed by the term with the second-highest degree, and so on, until we reach the constant term (a term without a variable).