5.1 Operations with Polynomials

Recall these properties of exponents

(2k)4=

(ab)3 =

A. Simplify the expression Assume that no variable equals 0.

B. Simplify the expression . Assume that no variable equals 0.

C. Simplify the expression . Assume that no variable equals 0.

A. Simplify the expression . Assume that no variable equals 0.

Definitions

Rules of Polynomial FunctionsThere are no square roots of variables,

no fractional powers, and no variables in the denominator of any fractions

A monomial is an expression with one term.

√𝑥

Important Vocabulary

The degree of a monomial is the sum of the powers of the variable

The degree of a polynomial is the degree of the monomial with the highest degree.

C. Determine whether is a polynomial. If it is a polynomial, state the degree of the polynomial.

To simplify Polynomials, add like terms

A. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6).

B. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2).

A. Simplify (3x2 + 2x – 3) – (4x2 + x – 5).

Use distributive Property

Find –y(4y2 + 2y – 3).

Find –x(3x3 – 2x + 5).

Find (a2 + 3a – 4)(a + 2).

Find (x2 + 3x – 2)(x + 4).

Write a polynomial equation

E-SALES A small online retailer estimates that the cost, in dollars, associated with selling x units of a particular product is given by the expression0.001x

2 + 5x + 500. The revenue from sellingx units is given by 10x. Write a polynomial to represent the profits generated by the product.