I am a problem solver Not a problem maker I am an answer giver not an answer taker I can do problems I haven’t seen I know that strict doesn’t equal mean.

Slides:

Advertisements

Similar presentations

Rational Algebraic Expressions

Advertisements

I am a problem solver Not a problem maker

EXAMPLE 3 Standardized Test Practice SOLUTION 8x 3 y 2x y 2 7x4y37x4y3 4y4y 56x 7 y 4 8xy 3 = Multiply numerators and denominators. 8 7 x x 6 y 3 y 8 x.

Chapter 6 – Polynomial Functions

Appendix B.4 Solving Inequalities Algebraically And Graphically.

Warm Up Simplify each expression. Factor the expression.

EXAMPLE 3 Simplify an expression by dividing out binomials Simplify x 2 – 3x – 10 x 2 + 6x + 8. State the excluded values. SOLUTION x 2 – 3x – 10 x 2 +

I am a problem solver Not a problem maker I am an answer giver not an answer taker I can do problems I haven’t seen I know that strict doesn’t equal mean.

9.1 Multiplying and Dividing Rational Expressions

Simplifying Rational Expressions.

Simplify Rational Algebraic Expressions In the previous section on polynomials, we divided a polynomial by a binomial using long division. In this section,

What does Factorial mean? For example, what is 5 factorial (5!)?

Warm-up Simplify. 5x x – a + 2b – (a – 2b) Multiply.

2.4 Use the Binomial Theorem Test: Friday.

Simplify Rational Expressions

 Inverse Variation Function – A function that can be modeled with the equation y = k/x, also xy = k; where k does not equal zero.

Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.

Chapter 9: Rational Expressions Section 9-1: Multiplying and Dividing Rationals 1.A Rational Expression is a ratio of two polynomial expressions. (fraction)

Factor Each Expression Section 8.4 Multiplying and Dividing Rational Expressions Remember that a rational number can be expressed as a quotient.

EXAMPLE 2 Multiply rational expressions involving polynomials Find the product 3x 2 + 3x 4x 2 – 24x + 36 x 2 – 4x + 3 x 2 – x Multiply numerators and denominators.

10-6 Dividing Polynomials Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

9-4 Multiplying and Dividing Rational Expressions (Day 1) Objective: Students will be able to simplify complex fractions.

Rational Expressions Simplifying Section Simplifying Rational Expressions The objective is to be able to simplify a rational expression.

Add & Subtract Rationals – Common Denominator To add or subtract rational expressions with common denominators: 1) Add or subtract the numerators 2) Write.

I am a problem solver Not a problem maker I am an answer giver not an answer taker I can do problems I haven’t seen I know that strict doesn’t equal mean.

9.5 The Binomial Theorem Let’s look at the expansion of (x + y)n

Notes Over 2.8 Rules for Dividing Negative Numbers. ( Same as Multiplying ) If there is an even number of negative numbers, then the answer is Positive.

Binomial Theorem Binomial Theorem Term 1 : Unit 3

9.4 Multiplying and Dividing Rational Expressions -To multiply and divide rational expressions. -Use rational expressions to model real life quantities.

8 4 Multiply & Divide Rational Expressions

Warm Up Add or subtract x ≠ x ≠ –1, x ≠ 1 Simplify. Identify any x-values for which the expression is undefined –

2-6 Binomial Theorem Factorials

Term 2 Week 7 Warm Ups. Warm Up 12/1/14 1.Identify all the real roots of the equation: 3x x 2 – 9x Identify whether the degree is odd or.

Quick Crisp Review Complex Numbers Conjugates What happens when you multiply conjugates?

MULTIPLYING RATIONAL NUMBERS LESSON 8. Multiplying Integers  Positive x Positive = Positive  Positive x Negative = Negative  Negative x Negative =

Rational Expressions Simplifying. Polynomial – The sum or difference of monomials. Rational expression – A fraction whose numerator and denominator are.

10.4 Addition and Subtraction: Like Denominators.

To simplify a rational expression, divide the numerator and the denominator by a common factor. You are done when you can no longer divide them by a common.

Chapter 11.2 Notes: Simplify Rational Expressions Goal: You will simplify rational expressions.

Holt Algebra Dividing Polynomials Warm Up Divide. 1. m 2 n ÷ mn x 3 y 2 ÷ 6xy 3. (3a + 6a 2 ) ÷ 3a 2 b Factor each expression. 4. 5x x.

9.4 Rational Expressions (Day 1). A rational expression is in _______ form when its numerator and denominator are polynomials that have no common factors.

Section 6.2 Multiplication and Division. Multiplying Rational Expressions 1) Multiply their numerators and denominators (Do not FOIL or multiply out the.

Warm-Up Exercises Perform the operation. 1. x x + 36 x 2 – x5x x 2 – 6x + 9 · x 2 + 4x – 21 x 2 + 7x ANSWERS x + 3 x – 12 ANSWERS 5 x – 3.

Factor the expression x – 5x2 3. x3 – 125 ANSWER 5x (2 – x)

Simplifying. Multiplying and Dividing Rational Expressions Remember that a rational number can be expressed as a quotient of two integers. A rational.

Section 8.5 The Binomial Theorem. In this section you will learn two techniques for expanding a binomial when raised to a power. The first method is called.

Chapter 6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 6-1 Rational Expressions and Equations.

Simplifying Rational Expressions.

Warm Up Add or subtract –

Warm Up Add or subtract –

Binomial Theorem and Pascal’s Triangle.

Homework Questions? Daily Questions: How do I Multiply Polynomials?

AIM: How do we simplify, multiply and divide rational expressions?

Simplifying Rational Expressions

8.1 Multiplying and Dividing Rational Expressions

7.1/7.2 – Rational Expressions: Simplifying, Multiplying, and Dividing

4.2 Pascal’s Triangle and the Binomial Theorem

9.5 The Binomial Theorem Let’s look at the expansion of (x + y)n

10.2b - Binomial Theorem.

8.4 Multiply & Divide Rational Expressions

Binomial Theorem Pascal’s Triangle

Use Pascal’s triangle to expand the expression (3 x - 2 y) 3

Simplifying Rational Expressions.

Simplifying Rational Expressions.

Homework Questions? Daily Questions: How do I Multiply Polynomials?

Simplifying Rational Expressions.

6.7 Dividing a Polynomial by a Polynomial

Unit 5 Polynomial Operations

Simplifying rational expressions

Presentation transcript:

I am a problem solver Not a problem maker I am an answer giver not an answer taker I can do problems I haven’t seen I know that strict doesn’t equal mean In this room we do our best Taking notes -practice –quiz- test The more I try the better I feel My favorite teacher is Mr. Meal…..ey

CONSTRUCTING THE TRIANGLE 1 ROW ROW ROW ROW R0W ROW ROW ROW ROW ROW 9 2

Pascal’s Triangle and the Binomial Theorem (x + y) 0 = 1 (x + y) 1 = 1x + 1y (x + y) 2 = 1x 2 + 2xy + 1y 2 (x + y) 3 = 1x 3 + 3x 2 y + 3xy 2 +1 y 3 (x + y) 4 = 1x 4 + 4x 3 y + 6x 2 y 2 + 4xy 3 + 1y 4 (x + y) 5 = 1x 5 + 5x 4 y + 10x 3 y x 2 y 3 + 5xy 4 + 1y 5 (x + y) 6 = 1x 6 + 6x 5 y x 4 y x 3 y x 2 y 4 + 6xy 5 + 1y

Expand the following. a) (3x + 2) 4 = 4 C 0 (3x) 4 (2) C 1 (3x) 3 (2) C 2 (3x) 2 (2) C 3 (3x) 1 (2) C 4 (3x) 0 (2) 4 n = 4 a = 3x b = 2 = 1(81x 4 )+ 4(27x 3 )(2)+ 6(9x 2 )(4)+ 4(3x)(8) + 1(16) = 81x x x x +16 b) (2x - 3y) 4 = 4 C 0 (2x) 4 (-3y) C 3 (2x) 1 (-3y) 3 = 1(16x 4 ) = 16x x 3 y + 216x 2 y xy y 4 n = 4 a = 2x b = -3y Binomial Expansion - Practice + 4 C 1 (2x) 3 (-3y) C 2 (2x) 2 (-3y) C 4 (2x) 0 (-3y) 4 + 4(8x 3 )(-3y)+ 6(4x 2 )(9y 2 )+ 4(2x)(-27y 3 )+ 81y 4

Match these up

Create a negative odd polynomial function and sketch the graph

Simplifying A rational expression is simplified or reduced to lowest terms when the numerator and denominator have no common factors other than 1. Examples:

Simplifying Rational Expressions 1.Factor both the numerator and denominator as completely as possible. 2.Divide out any factors common to both the numerator and denominator.

Factoring a Negative 1 Remember that when –1 is factored from a polynomial, the sign of each term in the polynomial changes. Example: – 2x + 5 = – 1(2x – 5) = –(2x – 5)