factoring unit day 1 – polynomials multiplying mrs. parziale
TRANSCRIPT
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Factoring Unit
Day 1 – PolynomialsMultiplying
Mrs. Parziale
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Introducing PolynomialsTerm Definition
Monomial
Is a number, a variable, or a product of a number and one or more variables
with whole number exponents.8 -2x 3x2y
Polynomial Is a monomial or a sum of monomials4x2 3x2 + 4x + 5
Binomial A polynomial with 2 terms x – 4 4y2 + 8
Trinomial A polynomial with 3 termsx2 – 3x + 10
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Definitions
• Degree of a polynomial – the highest sum of exponents for any one monomial of the polynomial.
• Find the degree of the given polynomial.
1. 3 2x 32. 4 17 5x x
3 23. 7 10 15x y xy
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More Definitions
• The leading coefficient of a polynomial is the coefficient of the variable with the ____________ exponent.
• The constant term of a polynomial is the term __________________.
largest
without a variable
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Yet Another Definition
• Standard form of a polynomial is when the terms are written so that the exponents on the variables decrease from left to right.
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Try These• Write the polynomial in standard form.
Identify the leading coefficient and constant terms of each.
2 34. 3 3 12x x x 3 25. 4 3x x
2 36. 7 6 3x x x
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Multiplication of Polynomials
• Part 1: Monomial x Monomial
3 47. ( )( )x x
3 2 5 28. ( )( )a b ab
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Part 2: Monomial x Polynomial
29. 5 ( 2 3)x x x
3 210. 4 (2 5 9)x x x
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Part 3: Binomial x Binomial
• Distribute, then combine like terms (FOIL)
11. (6 5)(3 4)x x 212. ( 4 )( 1)x x x
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Part 4: Polynomial x Polynomial
• Use the distributive property.
313. (3 2)(2 2 1)x x x
314. ( 5)(4 3 7)a a a
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Multiplying Special Polynomials
Special Product #1: Sum and Difference of 2 Terms
1. ( 4)( 4)x x 2 22. ( 3)( 3)x x
What is the pattern? (a + b)(a – b) = ___________
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Special Product #2: The Square of a Binomial
Multiplying Special Polynomials
23. (5 3)x 24. (3 7)x
4.
What is the pattern? (a + b)2 = _______________
What is the pattern? (a - b)2 = _______________
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Closure
• What is the degree of a polynomial?• What is a monomial, binomial, trinomial,
polynomial?• How do you multiply polynomials?• How do you multiply special polynomials, such
as:
( 6)( 6)x x 2( 7)x 2( 7)x