Adding, Subtracting, & Multiplying Polynomials

Front

What is a polynomial?

Back

A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. For example, 3x^2 + 2x - 5 is a polynomial.

Front

What are the degrees of polynomials?

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

How do you add polynomials?

Back

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

Front

How do you subtract polynomials?

Back

To subtract polynomials, distribute the negative sign and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 5x^2 - 2x^2 + 3 - 1 = 3x^2 + 2.

Front

What is a like term?

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, while 3x^2 and 4x are not.

Front

What is the process of combining like terms?

Back

Combining like terms involves adding or subtracting the coefficients of terms that have the same variable and exponent. For example, 2x + 3x = 5x.

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

How do you multiply polynomials?

Back

To multiply polynomials, use the distributive property or FOIL method for binomials. For example, (x + 2)(x + 3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

Front

What is the FOIL method?

Back

The FOIL method is a technique for multiplying two binomials. It stands for First, Outside, Inside, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

Front

What is a coefficient?

Back

A coefficient is a numerical factor in a term of a polynomial. For example, in 4x^3, 4 is the coefficient.