8.1 + and - polynomials:
DESCRIPTION
Monomial: a real number, a variable, or a product of both. Ex: 4, 4x, 18, -4x 2 , c, . 8.1 + AND - POLYNOMIALS:. Degree of monomial: The sum of the exponents of its variables. Ex: 4 Degree 0 4x Degree 1 -4x 2 Degree of 2 - PowerPoint PPT PresentationTRANSCRIPT
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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
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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
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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
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GOAL:
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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
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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
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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!
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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?
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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
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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
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VIDEOS:Polynomials
Adding and Subtracting
Polynomials:
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/addition-and-subtraction-of-polynomials
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CLASSWORK:
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Problems: As much as needed to master the concept