Practice - Polynomial Operations

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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^2 + 3x + 1 is a polynomial.

Front

What is a monomial?

Back

A monomial is a polynomial with only one term. For example, 5x^3 is a monomial.

Front

What does it mean to divide a polynomial by a monomial?

Back

Dividing a polynomial by a monomial involves dividing each term of the polynomial by the monomial.

Front

How do you subtract polynomials?

Back

To subtract polynomials, you subtract the coefficients of like terms. For example, (3x^2 + 4x) - (2x^2 + 5x) = (3-2)x^2 + (4-5)x = x^2 - x.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It is used to multiply a single term by a polynomial.

Front

What is the result of multiplying a polynomial by a monomial?

Back

When multiplying a polynomial by a monomial, you multiply each term of the polynomial by the monomial.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in 4x^3 + 2x^2 + 5, the degree is 3.

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What are like terms?

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

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What is the process of combining like terms?

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Combining like terms involves adding or subtracting the coefficients of like terms. For example, 2x + 3x = 5x.

Front

What is a coefficient in a polynomial?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^2, 4 is the coefficient.