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Algebra 81 Lesson with notes 2nd a.notebook
1
February 25, 2016
Feb 115:54 PM
81 Adding and Subtracting Polynomials
Learning Targets:I can write polynomials in standard formI can add and subtract polynomials
What is the value of t for the year 2007?
What would be the value of t for the year 2010?
Using the equation, find the value of U fo rthe year 2007.
How many monomials make up the expression that equals U?
What are they?
Feb 239:47 AM
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 116:03 PM
Polynomial: a monomial or the sum of monomials, each called a term.
Binomial: sum of two monomials
Trinomial: sum of three monomials
Degree of a monomial: the sum of the exponents of all its variables. A nonzero constant term has degree 0, and zero has no degree
Degree of a polynomial: the greatest degree of any term in the polynomial.
Feb 116:12 PM
Names of polynomials
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 116:15 PM
Feb 116:16 PM
Example 1: Determine whether each expression is a polynomial. If it is a polynomial, find the degree and determine whether it is a monomial, binomial, or trinomial.
1. 6x 4 2. x2 + 2xy 7 3. 26b2 4. 14d + 19e3 5d4
5. x 6. 3y2 2y + 4y 1 7. 5rx + 7tuv 8. 10x4 8xa
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 116:28 PM
Standard form of a polynomial: when terms are in order from greatest to least degree.
Leading coefficient: the coefficient of the first term when the polynomial is in standard form.
Feb 116:35 PM
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 116:38 PM
Example 2: Write each polynomial in standard form. Identify the leading coefficient.
9. 9x2 + 3x6 4x 10. 12 + 5y + 6xy + 8xy2
11. 8 2x2 + 4x4 3x 12. y + 5y3 2y2 7y6 + 10
Feb 116:45 PM
Adding polynomials: add like terms (must have the same variable(s) and the same exponents)
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 116:49 PM
Example 3: Find each sum.
13. (7y2 + 2y 3) + (2 4y + 5y2) 14. (4x2 2x + 7) + (3x 7x2 9)
15. (5x2 3x + 4) + (6x 3x2 3) 16. (y4 3y + 7) + (2y3 + 2y 2y4 11)
Feb 116:55 PM
Subtract polynomials: change all the signs of the one being subtracted, then combine like terms.
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 117:00 PM
Example 4: Find each difference.
17. (6y2 + 8y4 5y) (9y4 7y + 2y2) 18. (6n2 + 11n3 + 2n) (4n 3 + 5n2)
19. (4x3 3x2 + 6x 4) (2x3 + x2 2) 20. (8y 10 + 5y2) (7 y3 + 12y)
Feb 117:04 PM
Algebra 81 Lesson with notes 2nd a.notebook
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February 25, 2016
Feb 117:07 PM
Example 5:
21. The total amount of toy sales T (in billions of dollars) consists of two groups: sales of video games V and sales of traditional toys R. In recent years, the sales of traditional toys and total sales could be represented by the following equations, where n is the number of year since 2000.
R = 0.46n3 1.9n2 + 3n + 19T = 0.45n3 1.85n2 + 4.4n + 22.6
a. Write an equation that represents the sales of video games V.
b. Use the equation to predict the amount of video game sales in the year 2012.
