Polynomial Arithmetic

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 add polynomials?

Back

Adding polynomials involves combining like terms, which are terms that have the same variable raised to the same power.

Front

What does it mean to subtract polynomials?

Back

Subtracting polynomials involves subtracting the coefficients of like terms from each other.

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

Multiply: (2x + 3)(3x + 1)

Back

6x^2 + 11x + 3

Front

Subtract the polynomials: (2x + 12) - (5x - 8)

Back

-3x + 20

Front

Multiply: (x + 5)(x - 5)

Back

x^2 - 25

Front

Multiply: 5x(3x^2 + 2x - 7)

Back

15x^3 + 10x^2 - 35x

Front

Multiply: (3x + 6)(3x - 6)

Back

9x^2 - 36

Front

What are like terms?

Back

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