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, combined using addition, subtraction, and multiplication.

Front

What does it mean to add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients while keeping the variable part the same.

Front

What does it mean to subtract polynomials?

Back

To subtract polynomials, change the signs of the terms in the polynomial being subtracted and then combine like terms.

Front

What is a like term?

Back

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

Front

How do you multiply a polynomial by a monomial?

Back

To multiply a polynomial by a monomial, distribute the monomial to each term of the polynomial.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parenthesis.

Front

What is the result of (6x^2 + 10x - 9) - (4x^2 - 13)?

Back

2x^2 + 10x + 4.

Front

What is the result of (3 - 2x + 2x^2) - (4x - 5 + 3x^2)?

Back

-x^2 - 6x + 8.

Front

What is the result of (12x^2 + 3x^4 - 6x - 2) + (-3x^4 + 5x + 9 - 7x^2)?

Back

5x^2 - x + 7.

Front

How do you simplify (b + 3)(b^2 + 2b + 1)?

Back

b^3 + 5b^2 + 7b + 3.