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5.1 Operations with Polynomials

5.1 Operations with Polynomials. Recall these properties of exponents

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Page 1: 5.1 Operations with Polynomials. Recall these properties of exponents

5.1 Operations with Polynomials

Page 2: 5.1 Operations with Polynomials. Recall these properties of exponents

Recall these properties of exponents

Page 3: 5.1 Operations with Polynomials. Recall these properties of exponents

(2k)4=

(ab)3 =

Page 4: 5.1 Operations with Polynomials. Recall these properties of exponents
Page 5: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 6: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 7: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 8: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 9: 5.1 Operations with Polynomials. Recall these properties of exponents

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.

Page 10: 5.1 Operations with Polynomials. Recall these properties of exponents

√𝑥

Page 11: 5.1 Operations with Polynomials. Recall these properties of exponents

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.

Page 12: 5.1 Operations with Polynomials. Recall these properties of exponents
Page 13: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 14: 5.1 Operations with Polynomials. Recall these properties of exponents

To simplify Polynomials, add like terms

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

Page 15: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 16: 5.1 Operations with Polynomials. Recall these properties of exponents

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

Page 17: 5.1 Operations with Polynomials. Recall these properties of exponents

Use distributive Property

Find –y(4y2 + 2y – 3).

Page 18: 5.1 Operations with Polynomials. Recall these properties of exponents

Find –x(3x3 – 2x + 5).

Page 19: 5.1 Operations with Polynomials. Recall these properties of exponents

Find (a2 + 3a – 4)(a + 2).

Page 20: 5.1 Operations with Polynomials. Recall these properties of exponents

Find (x2 + 3x – 2)(x + 4).

Page 21: 5.1 Operations with Polynomials. Recall these properties of exponents

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.