Multiplication and Division of Polynomials

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, 3x^2 + 2x - 5 is a polynomial.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in another polynomial, then combining like terms.

Front

Simplify: 5a(a^2 + 3a - 4)

Back

5a^3 + 15a^2 - 20a

Front

Multiply: 3m^2n(4m^2 - 5n + 3)

Back

12m^4n - 15m^2n^2 + 9m^2n

Front

What is the quotient when m^2 - 9m - 10 is divided by m + 1?

Back

m - 10

Front

What is the quotient when m^2 + 9m + 14 is divided by m + 7?

Back

m + 2

Front

Multiply: (4a + 5)(5a - 7)

Back

20a^2 - 3a - 35

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 - x, the degree is 3.

Front

What are like terms 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

What is the process of dividing polynomials called?

Back

The process of dividing polynomials is called polynomial long division.