Multiplication and Division of Polynomials

Front

Define a polynomial.

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

What is the standard form of a polynomial?

Back

The standard form of a polynomial is written in descending order of the degree of its terms, from the highest degree to the lowest.

Front

What does it mean to simplify a polynomial expression?

Back

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

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

Multiply: 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 long division of polynomials?

Back

Long division of polynomials is a method used to divide a polynomial by another polynomial, similar to long division with numbers.

Front

Solve using long division: (x^2 + 2x - 63) ÷ (x + 9)

Back

x - 7

Front

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

Back

20a^2 - 3a - 35