factoring unit day 1 – polynomials multiplying mrs. parziale
TRANSCRIPT
Factoring Unit
Day 1 – PolynomialsMultiplying
Mrs. Parziale
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
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
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
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.
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
Multiplication of Polynomials
• Part 1: Monomial x Monomial
3 47. ( )( )x x
3 2 5 28. ( )( )a b ab
Part 2: Monomial x Polynomial
29. 5 ( 2 3)x x x
3 210. 4 (2 5 9)x x x
Part 3: Binomial x Binomial
• Distribute, then combine like terms (FOIL)
11. (6 5)(3 4)x x 212. ( 4 )( 1)x x x
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
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) = ___________
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 = _______________
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