Intro to Polynomials LT I will be able

Intro to Polynomials LT: I will be able to classify polynomials and write them in standard form. Success Criteria q I can classify polynomials q I can rearrange polynomials into standard form q I can describe the different parts of a polynomial Today’s Agenda ü Do Now ü Hand Back Quiz ü Lesson ü HW#22

Introduction to Polynomials

• Monomial: 1 term (axn with n is a nonnegative integers, a is a real number) Ex: 3 x, -3, or 4 xy 2 z • Binomial: 2 terms Ex: 3 x - 5, or 4 xy 2 z + 3 ab • Trinomial: 3 terms Ex: 4 x 2 + 2 x - 3

• Polynomial: is a monomial or sum of monomials Ex: 4 x 3 + 4 x 2 - 2 x - 3 or 5 x + 2 • Are these polynomials or not polynomials? 3/xy -2 xyab | x – 3| √x (1/2)x No yes No No Yes

• Degree: exponents • Degree of polynomial: highest exponent (if the term has more than 1 variable, then add all exponents of that term) • Coefficient: number in front of variables • Leading term: term of highest degree. Its coefficient is called the leading coefficient • Constant term: the term without variable • Missing term: the term that has 0 as its coefficient

• Ex: Term: -3 x 4 – 4 x 2 + x – 1 -3 x 4 , – 4 x 2 , x, – 1 Degree 4 2 1 0 Coefficient -3 -4 1 -1 Degree of this polynomial is 4 Leading term is -3 x 4 and -3 is the leading coefficient Constant term: is -1 Missing term (s): is x 3

• Ex 2: Term: -6 x 9– 8 x 6 y 4 + x 7 y + 3 xy 5 - 4 -6 x 9, – 8 x 6 y 4 , x 7 y , 3 xy 5 , - 4 Degree 9 10 8 6 0 Coefficient -6 -8 1 3 -4 Degree of this polynomial is 10 Leading term is – 8 x 6 y 4 and -8 is the leading coefficient Constant term: is -4

• Descending order: exponents decrease from left to right • Ascending order: exponents increase from left to right • When working with polynomials, we often use Descending order

• Arrange in descending order using power of x 1) -6 x 2 – 8 x 6 + x 8 + 3 x - 4 = x 8– 8 x 6 - 6 x 2 + 3 x - 4 2) 5 x 2 y 2 + 4 xy + 2 x 3 y 4 + 9 x 4 = 9 x 4 + 2 x 3 y 4 + 5 x 2 y 2 + 4 xy

• Opposites of Polynomials: 1) 2 x Opposite is -2 x 2) 3 x 4 – 4 x 2 + x Opposite is - 3 x 4 + 4 x 2 - x

Adding and Subtracting Polynomials • Same as combining like-term: Add or subtract only numbers and keep the same variables

1) (-6 x 4 – 8 x 3 + 3 x - 4) + (5 x 4 + x 3 + 2 x 2 -7 x) = -6 x 4 + 5 x 4 – 8 x 3 + 2 x 2 + 3 x -7 x -4 = -x 4 - 7 x 3 + 2 x 2 - 4 x -4

2) (-6 x 4 – 8 x 3 + 3 x - 4) - (5 x 4 + x 3 + 2 x 2 -7 x) = -6 x 4 – 8 x 3 + 3 x - 4 - 5 x 4 - x 3 - 2 x 2 +7 x = -11 x 4 - 9 x 3 - 2 x 2 +10 x -4

HW#22