Polynomials Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 2x^3 + 3x^2 - 5 is a polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is when the terms are arranged in descending order of their degree. For example, 9x^3 + 8x^2 - 3x - 11 is in standard form.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (2x^2 + 3x) + (4x^2 + 5) = (2x^2 + 4x^2) + 3x + 5 = 6x^2 + 3x + 5.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x, the degree is 3.

Front

What is polynomial long division?

Back

Polynomial long division is a method used to divide a polynomial by another polynomial of the same or lower degree, similar to numerical long division.

Front

What is a leading coefficient?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. For example, in 5x^4 + 3x^2 - 2, the leading coefficient is 5.

Front

What are like terms?

Back

Like terms are terms in a polynomial that have the same variable raised to the same power. For example, 3x^2 and 5x^2 are like terms.

Front

What is the result of dividing (2x^3 + 5x^2 + 9) by (x + 3)?

Back

The result is 2x^2 - x + 3.

Front

What is the result of adding (6n^2 - 7n^4 + 8) and (6 + 8n + 4n^4)?

Back

The result is -3n^4 + 6n^2 + 8n + 14.

Front

What is the result of dividing (-2x^2 + 4x + 48) by (x + 4)?

Back

The result is -2x + 12.