Lesson 5-1/5-2 Polynomials

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Lesson 5-1/5-2Polynomials Adding/Subtracting

• Objective
• Students will
• Evaluate polynomial functions
• Simplify polynomials by collecting like terms
• Add/Subtract polynomials
• Find the additive inverse of polynomials

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Polynomials A collection of terms 2x 3x
4 x3 2x2y 8 Coefficients numbers in front
of each term Degree of a term sum of exponents
acting on the variables Degree of polynomials
equal to highest degree of any term Names
monomial, binomial, trinomial
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General form (descending order) anxn
an-1xn-1 a1x a0 Polynomial Functions
Evaluate by plugging in P(x) x2 5x 8
when x 6 P(6) 62 5(6) 8
14 Simplifying Polynomials combine like terms
(same variable parts)
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Example 1 Simplify, state the degree, and give
the specific name. 2x2y 4x 4y 3xy2 x
2x2y 3xy2 3x 4y Degree 3 (x2y1 21)
Name More than 3 terms so just polynomial will
do!
Adding/Subtracting Polynomials Combine like
terms A) Mark like terms Or B) line up
vertically Additive Inverse Polynomial with all
opposite terms EX 2x2 -3x 5 Additive
inverse -2x2 3x -5 When problem is
subtraction, Change to add the inverse!!!
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Example 2 Subtract (change to additive
inverse) Method A) Mark LikeTerms (4xy2 6x2y2
5x3y2) (2xy2 4x2y2 8x3y2) (4xy2 6x2y2
5x3y2) (-2xy2 - 4x2y2 8x3y2) 2xy2 -
10x2y2 13x3y2)
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• Example 2 Subtract (change to additive inverse)
• Method B) Line up Vertically
• (4xy2 6x2y2 5x3y2) (2xy2 4x2y2 8x3y2)

(4xy2 6x2y2 5x3y2) (-2xy2 - 4x2y2
8x3y2)
2xy2 - 10x2y2 13x3y2
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You Try

• (5xy4 - 7xy2 4x2 - 3) (-3xy4 2xy2 - 2y 4)

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Assignment
5-1/208 / 3- 31 eoo, 41-49o
5-2/ 212-213/1-29 eoo, 37, 45