Do Now 2/22/10Do Now 2/22/10

• Copy HW in your planner.Copy HW in your planner.– Text p. 557, #4-28 multiples of 4, #32-Text p. 557, #4-28 multiples of 4, #32-

35 all35 all

• In your notebook on a new page define the In your notebook on a new page define the parts of the expression below. Use the parts of the expression below. Use the following words: terms, coefficients, following words: terms, coefficients, constants, exponentsconstants, exponents

-3x² + 2x + 8-3x² + 2x + 8

Chapter 9 “Polynomials and Factoring”Chapter 9 “Polynomials and Factoring”• (9.1) (9.1) Add and subtract polynomialsAdd and subtract polynomials

• (9.2) (9.2) Multiply polynomialsMultiply polynomials

• (9.3) (9.3) Find special products of polynomialsFind special products of polynomials

• (9.4) (9.4) Solve polynomial equations in factored formSolve polynomial equations in factored form

• (9.5) (9.5) Factor x² + bx + cFactor x² + bx + c

• (9.6) (9.6) Factor ax² + bx + cFactor ax² + bx + c

• (9.7) (9.7) Factor special productsFactor special products

• (9.8) (9.8) Factor polynomials completelyFactor polynomials completely

Parts of an ExpressionParts of an Expression

-3x-3x²² + 2x + 8 + 2x + 8TermsTerms of the expression

CoefficientCoefficient the number part of the term (negative sign included)

ConstantConstant Term that has no variable

Remember this???

Remember this???

ObjectiveObjective• SWBAT add and subtract

polynomials

Section 9.1 “Add and Subtract Section 9.1 “Add and Subtract Polynomials” Polynomials”

MonomialMonomiala number, a number,

-3x-3xthe sum of the exponents of the variables in the monomial

Degree of a MonomialDegree of a Monomial

xx³³yyz²z²

or the product of a or the product of a number and one or more variables with number and one or more variables with whole whole numbernumber exponents exponents

a variable, a variable,

77Degree = 1

Degree = 6

Degree = 0

PolynomialPolynomiala monomial, a monomial,

––3x3xthe greatest degree of its termsDegree of a PolynomialDegree of a Polynomial

– – xx³³

or the sum (or difference) of monomialsor the sum (or difference) of monomials

+7+7Degree = 1 Degree = 3Degree = 0

Leading CoefficientLeading Coefficient the coefficient of the first term when the coefficient of the first term when exponents are decreasing from left to right.exponents are decreasing from left to right.

Write a Write a polynomial with polynomial with exponents exponents decreasing decreasing from left to right.from left to right.

-1-1

Types of PolynomialsTypes of Polynomials

Binomial Binomial

4 – 3x4 – 3xpolynomial with 2 termspolynomial with 2 terms

2x2x³³+ x – 7+ x – 7

Trinomial Trinomial polynomial with 3 termspolynomial with 3 terms

To Be or Not To Be a Polynomial…To Be or Not To Be a Polynomial…

14 – 3x14 – 3x Yes; 1Yes; 1stst degree binomial degree binomial

4x4x³³ Yes; 3Yes; 3rdrd degree monomial degree monomial

2y2y No; negative exponentNo; negative exponent-3-3

9 + 3x9 + 3x² + 2yz³² + 2yz³Yes; 4Yes; 4thth degree trinomial degree trinomial

6x + 2x6x + 2x No; variable exponentNo; variable exponentnn

Add PolynomialsAdd Polynomials

(2x(2x²² + x + x³³ – 1) – 1)

Like TermsLike Terms terms that have the same variable

(2x(2x³ – 5x²³ – 5x² + x) + x) + + You can add polynomials using the vertical or horizontal format.You can add polynomials using the vertical or horizontal format.

Vertical FormatVertical Format

2x2x³ – 5x²³ – 5x² + x + x

x³ + 2xx³ + 2x²² – 1 – 1

3x3x³ – 3x²³ – 3x² + x – 1 + x – 1

Horizontal FormatHorizontal Format

((2x2x³³ + x³+ x³) + () + (2x²2x² – 5x²– 5x²)) + x+ x – 1– 1

3x3x³ – 3x²³ – 3x² + x – 1 + x – 1

Subtract PolynomialsSubtract Polynomials

(-2n(-2n²² + 2n – 4) + 2n – 4)

Like TermsLike Terms terms that have the same variable

(4n(4n²² + 5) + 5) – –You can subtract polynomials using the vertical or horizontal format.You can subtract polynomials using the vertical or horizontal format.

Vertical FormatVertical Format

4n4n²² + 5 + 5

– – (-2n(-2n²² +2n – 4) +2n – 4)

Horizontal FormatHorizontal Format

((4n²4n² + 2n²+ 2n²)) – 2n– 2n + ( + (55 + 4+ 4))

6n6n²² – 2n + 9 – 2n + 9 +(2n+(2n²² -2n + 4) -2n + 4)

6n6n²² – 2n + 9 – 2n + 9

Adding and Subtracting Polynomials

)18()35( 22 aa

)122()2( 232 nnnnn

413

)13()85(2

22

a

aa

122

12)2()(23

223

nn

nnnnn

Simplifying Polynomials in Simplifying Polynomials in GeometryGeometry

• What is the perimeter of the trapezoid?

3x – 2

5x – 2

2x 2x + 1

Perimeter is thePerimeter is thedistance around a figure.distance around a figure.

3x - 2 + 2x + 2x + 1 + 5x - 23x - 2 + 2x + 2x + 1 + 5x - 2 (reorder terms)(reorder terms)

Add together each of the sides.Add together each of the sides.

3x + 2x + 2x + 5x – 2 – 2 + 13x + 2x + 2x + 5x – 2 – 2 + 1(combine like terms)(combine like terms)

12x – 3 12x – 3

HomeworkHomework

Text p. 557, Text p. 557,

#4-28 multiples of 4, #32-35 #4-28 multiples of 4, #32-35 allall