Polynomial Operations

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^2 + 3x + 5 is a polynomial.

Front

What does it mean to simplify a polynomial expression?

Back

Simplifying a polynomial expression means to combine like terms and reduce the expression to its simplest form.

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 4x^3 + 2x^2 + x, the degree is 3.

Front

How do you multiply two polynomials?

Back

To multiply two polynomials, use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.

Front

What is the result of multiplying (x + 2)(x + 3)?

Back

The result is x^2 + 5x + 6.

Front

What is the formula for the square of a binomial?

Back

The formula for the square of a binomial (a + b)^2 is a^2 + 2ab + b^2.

Front

What is the product of (x + 5)^2?

Back

The product is x^2 + 10x + 25.

Front

What does it mean to expand a polynomial expression?

Back

Expanding a polynomial expression means to multiply out the factors and write the expression as a sum of terms.

Front

What is a like term in a polynomial?

Back

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

Front

How do you combine like terms?

Back

To combine like terms, add or subtract the coefficients of the terms that have the same variable and exponent.