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5.2 Polynomials Like terms FOIL method
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Definition of a Poly Poly- \Pol"y-\ [See Full, a.] A combining form or prefix from Gr. poly`s, many; as, polygon, a figure of many angles; polyatomic, having many atoms; polychord, polyconic. [1913 Webster] Also, polymorphic, polyester, polyamorous.
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Definition of a Polynomial
A polynomial is an expression made with many constants, variables and exponents, which are combined using addition, subtraction and multiplication, ... but not division.
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Degree of a polynomial In a polynomial you find the terms with the highest exponent or addition of exponents; these would be the degree of the polynomial.
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Like Terms Terms that are fond of each other
Terms with the same variable and exponent. 5x4y3 8x4y3 What can you do with like terms?
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Adding Like terms When you add like terms, you add their coefficients.
5x4y3 + 8x4y3 = (5 + 8)x4y3 = 13x4y3 You do not add the exponents. Why?
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Adding and Subtracting polynomials
Remove the parentheses by distributing the number in front. In this case it is a one. Then add the like terms
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What about Subtracting
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Multiply Polynomials We use the distributive property to multiply a monomial times binomial, trinomial or any polynomial.
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Multiplying a binomial by a binomials
Here we double distributive or more often call FOIL
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Multiply using FOIL (x – 5)(x + 2) x2 + 2x – 5x – 10 x2 -3x - 10
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Multiply using FOIL (x – 5)(x + 2) x2 + 2x – 5x – 10 x2 -3x - 10
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Multiply (x + 3)(x2 – 5x + 10)
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Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x
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Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x + 3x2 – 15x + 30
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Multiply (x + 3)(x2 – 5x + 10) x3 – 5x2 + 10x + 3x2 – 15x + 30
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Homework Page 231 – 232 # 17 – 33 odd, # 37 – 45 odd
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Homework Page 231 – 232 # 22 – 32 even, # 38 – 50 even
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