8.1 + AND - POLYNOMIALS: Monomial: a real number, a variable, or a product of both. Degree of...

8.1 + AND - POLYNOMIALS:Monomial: a real number, a variable, or a product of both.Ex: 4, 4x, 18, -4x2, c,

Degree of monomial: The sum of the exponents of its variables.

Ex: 4 Degree 0 4x Degree 1

-4x2 Degree of 2 6x3y2 Degree of 5

Polynomial: a monomial or a sum of monomials.Ex: 4 + C, 4x - 18, -4x2 + c -

Standard Form of a Polynomial: Polynomials written in descending order according to their degree

Ex: 1) -4x2 + 5x - 4 2) 5x3 + 11x + 6

3) 6y5 + 7y3 - 3y + 8

Degree of Polynomial in one variable: The same as the degree of the monomial with the highest degree.

Ex: 1) -4x2 + 5x - 4 Degree 2 2) 5x3 + 11x + 6 Degree 3

3) 6y5 + 7y3 - 3y + 8 Degree 5

GOAL:

CLASSIFY: To classify a polynomial we look at the degree and the number of terms (monomials) it contains:

Polynomial Degree Name Using Degree

Number of Terms

Name Using number of

Terms

6 0 Constant 1 Monomial

5x + 9 1 Linear 2 Binomial4x2+7x+ 6 2 Quadratic 3 Trinomial 7x3 3 Cubic 1 Monomial

3x4-4x-2 4 Fourth Degree 3 Trinomial

CLASSIFY: To classify a polynomial we must simplify.SIMPLIFYING POLYNOMIALS: To classify a polynomial we must simplify by adding and/or subtracting like terms:

Ex: Classify the following polynomials:

1) 3x2 + 5x2 - 3

2) 2x4 - 5x2 + 3x2 – 7x + x3) 4x – 1 + 5x3 + 7x – x3

SIMPLIFYING POLYNOMIALS: To classify a polynomial we must simplify by adding and/or subtracting like terms:

1) 3x2 + 5x2 - 3

2) 2x4 - 5x2 + 3x2 – 7x + x

3) 4x – 1 + 5x3 + 7x – x3

8x2 - 3 Quadratic Binomial

2x4 – 2x2 – 6x

Fourth Degree Trinomial

4x3 + 11x – 1

Cubic Trinomial

Notice: Must put in standard form before classifying!

REAL-WORLD (ADDITION): We can add/subtract polynomials by adding like terms:

Ex: A researcher studied the number of

overnight stays in the US National Park Service campgrounds and in the backcountry of the national park system over a 5-yr period. He

model his results as following:Campground = – 7.1x2 – 180x + 5800

Backgcountry = 21x2 – 140x + 1900What is the total number of stays?

Solution: We can add/subtract polynomials by adding like terms:

Campground – 7.1x2 – 180x + 5800

13.9x2 – 320x + 7700

Backgcountry 21x2 – 140x + 1900

Total stays: 13.9x2 – 320x + 7700

SUBTRACTION: We must not forget to distribute then add/subtract:

(x3 – 3x2+5x) – (7x3+5x2 – 12)

x3 – 3x2 + 5x – 7x3 – 5x2 + 12

– 6x3 – 8x2 +5x + 12

Classify: Cubic 4th term polynomial

VIDEOS:Polynomials

Adding and Subtracting

Polynomials:

https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/addition-and-subtraction-of-polynomials

CLASSWORK:

Page 477-479:

Problems: As much as needed to master the concept