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 are the degrees of polynomials?

Back

The degree of a polynomial is the highest power of the variable in the expression. For example, in the polynomial 4x^3 + 2x^2 - x + 5, the degree is 3.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (3x^2 + 2x) + (4x^2 + 5) = (3x^2 + 4x^2) + 2x + 5 = 7x^2 + 2x + 5.

Front

What is the process for subtracting polynomials?

Back

To subtract polynomials, distribute the negative sign to the second polynomial and then combine like terms. For example, (5x^2 + 3) - (2x^2 + 1) = 5x^2 + 3 - 2x^2 - 1 = 3x^2 + 2.

Front

What is the distributive property in relation to polynomials?

Back

The distributive property states that a(b + c) = ab + ac. This property is used to multiply a polynomial by a monomial or another polynomial.

Front

How do you multiply two binomials?

Back

To multiply two binomials, use the FOIL method: First, Outer, Inner, Last. For example, (a + b)(c + d) = ac + ad + bc + bd.

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, while 3x^2 and 4x are not.

Front

What is the result of multiplying (5h - 3)(3h + 7)?

Back

The result is 15h^2 + 26h - 21.

Front

How do you simplify the expression (–7x – 5x^4 + 5) – (–7x^4 – 5 – 9x)?

Back

The simplified expression is 2x^4 + 2x + 10.

Front

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

Back

The result is 2x^2 + 10x + 4.