Term 2 Week 7 Warm Ups. Warm Up 12/1/14 1.Identify all the real roots of the equation: 3x 3 - 18x 2 – 9x + 132 2.Identify whether the degree is odd or.

Slides:

Advertisements

Similar presentations

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

Advertisements

Chapter 6 – Polynomial Functions

Investigating Graphs of Polynomial Functions 6-7

The factor theorem The Factor Theorem states that if f(a) = 0 for a polynomial then (x- a) is a factor of the polynomial f(x). Example f(x) = x 2 + x -

( ) EXAMPLE 3 Solve ax2 + bx + c = 0 when a = 1

Investigating Graphs of Polynomial Functions 6-7

Chapter 4 – Polynomials and Rational Functions

C. Higher Functions Pre-Calculus 30.

Remainder and Factor Theorem Unit 11. Definitions Roots and Zeros: The real number, r, is a zero of f(x) iff: 1.) r is a solution, or root of f(x)=0 2.)

General Results for Polynomial Equations

Investigating Graphs of Polynomial Functions 6-7

Warm Up Divide using long division ÷ ÷

Warm Up Solve using synthetic OR long division Polynomial Functions A polynomial is written in standard form when the values of the exponents are.

4-1 Polynomial Functions

Lesson 4-1 Polynomial Functions.

7.5.1 Zeros of Polynomial Functions

Finding Real Roots of Polynomial Equations

ACTIVITY 34 Review (Sections ).

Quiz Show. Polynomial Operations 100ABCDE Evaluating Polynomials 200ABCDE Factoring & Solving Polynomials 300ABCDE App. Problems & Theorems 400ABCDE Polynomial.

Objectives Identify the multiplicity of roots Use the Rational Root Theorem and the Irrational Root Theorem to solve polynomial equations.

Algebra 2.  Warm Up  A monomial is an expression that is either a real number, a variable or a product of real numbers and variables.  A polynomial.

Test Wednesday Review Answers.

The Remainder and Factor Theorems. Solve by Using Long Division Example 1Example 2.

Warm Up Identify all the real roots of each equation. –1, 4 1. x 3 – 7x 2 + 8x + 16 = x 3 – 14x – 12 = 0 1, –1, 5, –5 3. x 4 + x 3 – 25x 2 – 27x.

Today in Pre-Calculus Go over homework Notes: Remainder and Factor Theorems Homework.

Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.

WARM-UP: 10/30/13 Find the standard form of the quadratic function. Identify the vertex and graph.

Section 4-3 The Remainder and Factor Theorems. Remainder Theorem Remainder Theorem – If a polynomial P(x) is divided by x-r, the remainder is a constant,

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

2.3 Real and Non Real Roots of a Polynomial Polynomial Identities Secondary Math 3.

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

6-5 & 6-6 Finding All Roots of Polynomial Equations Warm Up: Factor each expression completely. 1. 2y 3 + 4y 2 – x 4 – 6x 2 – : Use factoring.

Chapter 4: Polynomial and Rational Functions. 4-2 Quadratic Equations For a quadratic equation in the form ax 2 + bx + c = 0 The quadratic Formula is.

PreCalculus Section 2.6 Solve polynomial equations by factoring and the Rational Roots Theorem. Solve by factoring: x 3 + 5x 2 – 4x – 20 = 0 x 6 – x 3.

Solving polynomial equations

Remainder and Factor Theorems Unit 11. Definitions The real number, r, is a zero of f(x) iff:  r is a solution, or root, of f(x)=0  x-r is a factor.

Factoring Quadratic Expressions ax 2 + bx + c “SPLITTING THE MIDDLE” Feb. 27, 2014.

Section 3-7 Investigating Graphs of Polynomial Functions Objectives: Use properties of end behavior to analyze, describe, and graph polynomial functions.

Term 1 Week 8 Warm Ups. Warm Up 9/28/15 1.Graph the function and identify the number of zeros: 2x 3 – 5x 2 + 3x – 2 (Hit the y = ) 2.Identify the expressions.

Warm Up Divide using long division, if there is a remainder put it as a fraction ÷ ÷ x + 5y 23 7a – b Divide. 6x – 15y 3 7a 2.

Holt Algebra Dividing Polynomials 6-3 Dividing Polynomials Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson.

Chapter 6 - Polynomial Functions

Divide using long division.

Warm Up Divide using long division ÷ ÷ 2.1 Divide.

Dividing Polynomials 6-3 Warm Up Lesson Presentation Lesson Quiz

Warm-ups Week 8 10/8/12 Find the zeros of f(x) = x3 + 2x2 – 13x + 10 algebraically (without a graphing calculator). What if I told.

Chapter Polynomials of Higher Degree

Warm Ups Term 2 Week 6.

Warm Up Divide using long division ÷ ÷

4.3 The Remainder & Factor Theorems

Objectives Use properties of end behavior to analyze, describe, and graph polynomial functions. Identify and use maxima and minima of polynomial functions.

7.5 Zeros of Polynomial Functions

Describe End Behavior.

Dividing Polynomials Warm Up Lesson Presentation Lesson Quiz

Warm Up 1. Divide f(a) = 4a2 – 3a + 6 by a – 2 using any method.

4.2 Properties of Polynomial Graphs

If a polynomial q(x) is divided by x – 4, the quotient is 2

Warm-up: Find the equation of a quadratic function in standard form that has a root of 2 + 3i and passes through the point (2, -27). Answer: f(x) = -3x2.

Graphing Polynomials Unit 1D Day 19.

Dividing Polynomials 6-3 Warm Up Lesson Presentation Lesson Quiz

The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

Dividing Polynomials 6-3 Warm Up Lesson Presentation Lesson Quiz

Warm Up Identify all the real roots of each equation.

Dividing Polynomials 6-3 Warm Up Lesson Presentation Lesson Quiz

Warm Up Identify all the real roots of each equation.

21 = P(x) = Q(x) . (x - r) + P(r) 4.3 The Remainder Theorem

Describe End Behavior.

Preview to 6.7: Graphs of Polynomial

Dividing Polynomials 6-3 Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

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 even, whether the leading coefficient is positive or negative, describe the end behavior, and sketch the graph without using the calculator: 2x 3 + 3x 2 - 4x

Warm Up 12/2/14 3.Write the polynomial that has roots 3 and 5 + i. 4.Expand using Pascal’s triangle and the binomial theorem: (2x – 3) 4

Warm Up 12/3/14 5. Write the polynomial that has roots - 2 and √3. 6.Identify the roots of the equation. State the multiplicity of each root. x 3 + 5x 2 – 8x - 48

Warm Up 12/4/14 7. Write the polynomial that has roots - 2 and 5 + i. 8. If p(x) = 3x x 2 – 9x and q(x) = 2x 3 + 3x 2 - 4x, then what is p(x) – 3q(x)?

Warm Up 12/5/14 9. If the area of a rectangle is 6x 2 – 7x – 5 and the length is 3x – 5, write an expression that represents the width. (Hint: do long division!) 10. If a(x) = 2x x 2 – 9x + 42 and b(x) = 6x 3 + 7x 2 - x, then what is a(x) – 4b(x)?