Problem of the Day. Division and Rational Root Theorem TS: Making decisions after reflection and review Obj: Review polynomial division and how to find.

Slides:

Advertisements

Similar presentations

5.5: Polynomial Long Division and Synthetic Division

Advertisements

Agenda – Jan 6  Do Now  Review Reading  Notes: Rational Root Theorem  Work Time Due NEXT CLASS: Rational Root Theorem By the end of today’s class,

6.3 Dividing Polynomials. Warm Up Without a calculator, divide the following Solution:

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

Section 5.5 – The Real Zeros of a Rational Function

Objective Video Example by Mrs. G Give It a Try Lesson 6.6  Find the rational and real zeros of a polynomial function.

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

The Remainder and Factor Theorems Check for Understanding 2.3 – Factor polynomials using a variety of methods including the factor theorem, synthetic division,

EXAMPLE 2 Find all real zeros of f (x) = x 3 – 8x 2 +11x SOLUTION List the possible rational zeros. The leading coefficient is 1 and the constant.

The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.

Obj: To solve equations using the Rational Root Theorem.

2.3 Synthetic Substitution OBJ:  To evaluate a polynomial for given values of its variables using synthetic substitution.

Factor Theorem & Rational Root Theorem

Rational Root Theorem By: Yu, Juan, Emily. What Is It? It is a theorem used to provide a complete list of all of the possible rational roots of the polynomial.

Quick Crisp Review Zeros of a polynomial function are where the x-intercepts or solutions when you set the equation equal to zero. Synthetic and long division.

2.3 Real Zeros of Polynomial Functions 2015 Digital Lesson.

Homework Lesson 2.3 Read: Pages Page 127: #1-61 (EOO)

7.6 Rational Zero Theorem Algebra II w/ trig. RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be.

Section 3.3 Real Zeros of Polynomial Functions. Objectives: – Use synthetic and long division – Use the Remainder and Factor Theorem – Use the Rational.

Dividing Polynomials & The Remainder Theorem. Dividing Polynomials When dividing a polynomial by a monomial, divide each term in the polynomial by the.

Section 3.3 Theorems about Zeros of Polynomial Functions.

Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.

Section 5.5 The Real Zeros of a Polynomial Function.

Algebra II Explorations Review ( ) Day Divide using LONG Division. Show all work. Answer:

a. b.  To simplify this process, we can use a process called division.  Synthetic division works when dividing a polynomial by.  To get started, make.

Solving Polynomials. What does it mean to solve an equation?

7.6 Rational Zero Theorem Objectives: 1. Identify the possible rational zeros of a polynomial function. 2. Find all the rational zeros of a polynomial.

6.5 Day 1 Rational Zeros Theorem. If is in simplest form and is a rational root of the polynomial equation With integer coefficients, then p must be a.

LESSON 5.6 Rational Zeros of Polynomial Functions.

2.3 Real Zeros of Polynomial Functions 2014/15 Digital Lesson.

Warmup Divide using synthetic division using the zero given. Then factor the answer equation completely and solve for the remaining zeroes. Show.

Polynomial and Synthetic Division Objective: To solve polynomial equations by long division and synthetic division.

9.8 Day 2 – Finding Rational Zeros. The Rational Zero Theorem: If has integer coefficients, then every rational zero of f have the following form:

Solving Polynomials. Factoring Options 1.GCF Factoring (take-out a common term) 2.Sum or Difference of Cubes 3.Factor by Grouping 4.U Substitution 5.Polynomial.

Polynomials. DegreeNameExample 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic Some of the Special Names of the Polynomials of the first few degrees:

Polynomial Long Division

STD 3: To divide polynomials using long division and synthetic division and the rational root theorem Warm Up /15.

Section 3.4 Zeros of Polynomial Functions. The Rational Zero Theorem.

Algebra Finding Real Roots of Polynomial Equations.

Dividing Polynomials Two options: Long Division Synthetic Division.

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.

Warm Up Compute the following by using long division.

3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6x

Factor Theorem & Rational Root Theorem

Rational Root Theorem and Fundamental Theorem of Algebra

Real Zeros Intro - Chapter 4.2.

Rational Root Theorem and Fundamental Theorem of Algebra

Finding Real Roots of Polynomial Equations

7.1: Finding Rational Solutions of Polynomial Equations

The Rational Zero Theorem

Rational Root Theorem Math 3 MM3A1.

Notes 5.6 (Day 1) Find Rational Zeros.

Section 3.4 Zeros of Polynomial Functions

Finding Zeros of Polynomials

The Rational Zero Theorem

Remainder and Factor Theorem

Factor Theorem & Rational Root Theorem

Homework Check page 367 #

The Fundamental Theorem of Algebra And Zeros of Polynomials

Factor Theorem & Rational Root Theorem

The Rational Zero Theorem

“You wasted $150,000 on an education you coulda got for $1

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 5-5 and 5-6 (The Fundamental Theorem of Algebra), Descrates' Rule of Signs ALGEBRA II HONORS/GIFTED.

Digital Lesson Polynomial Functions.

Section 2.4: Real Zeros of Polynomial Functions

Digital Lesson Polynomial Functions.

Presentation transcript:

Problem of the Day

Division and Rational Root Theorem TS: Making decisions after reflection and review Obj: Review polynomial division and how to find the roots of polynomials Warm-Up: Think back to Algebra 2, what we have done so far and what you know about zeros and points on a function and answer the following. Find the cubic equation with zeros of -2, 1 and 5 and passes through the point (-1, 24)

Two kinds of division: Long Division – When is it used? Synthetic Division – When is it used?

Synthetic Division vs. Long Division 1) (x7 + 1) ÷ (x + 1) 2)(5x3 + 6x + 8) ÷ (x + 2) 3) (4x4 + 8x) ÷ (x2 – 1)

The Remainder Theorem If a polynomial f(x)is divided by x – k, the remainer is r = f(k). Rational Root Theorem If the polynomial f(x) = anxn + an-1xn-1 + … + a2x2 + a1x + a0 Has integer coefficients, every rational zero of f has the form Rational zero = Where p and q have no common factors other than 1, p is a factor of the constant term a0 and q is a factor of the leading coefficient an

Given P(x) = x6 – 2x4 + x3 – 5x2 + 1 Find P(2)

Given f(x) = x3 – 2x2 +a x – 4 If f(2) = 4, what is a?

Factor x3 + 3x2 – 10x – 24

Find all the zeros of x5 – x4 – 3x3 + 5x2 - 2x = 0

Now You Try: 1) Fully factor 8x4 – 14x3 – 71x2 – 10x + 24 (How do I check my solution with my calc I wonder???) 2) What is the remainder of (x-3)(x-4)(x-1)4 divided by x?