Operating with 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, 4x^2 + 3x - 5 is a polynomial.

Front

What does it mean to multiply polynomials?

Back

Multiplying polynomials involves using the distributive property to combine each term in one polynomial with each term in the other polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by each term in a polynomial.

Front

Find the product: (4x - 1)(3x^2 - 2x + 5)

Back

12x^3 - 11x^2 + 22x - 5

Front

Find the product: 3x(2x^2 + 9x + 6)

Back

6x^3 + 27x^2 + 18x

Front

Find the product: (4x + 1)(5x - 2)

Back

20x^2 - 3x - 2

Front

Find the product: (x - 3)(6x - 2)

Back

6x^2 - 20x + 6

Front

What is the difference of polynomials?

Back

The difference of polynomials is found by subtracting the corresponding coefficients of like terms from each polynomial.

Front

Find the difference: (3 - 2x + 2x^2) - (4x - 5 + 3x^2)

Back

-x^2 - 6x + 8

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.