2.5 Zeros of Polynomial Functions

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,

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.

5.5 Apply the Remainder and Factor Theorem

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.

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

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.

7.5.1 Zeros of Polynomial Functions

Polynomial Review OBJ: SWBAT analyze and graph polynomials.

6.9 Rational Zero Theorem Parts of a polynomial function f(x) oFactors of the leading coefficient = q oFactors of the constant = p oPossible rational roots.

Warm - Up Find the Vertex of f(x) = x 2 – 2x + 4.

5.4 – Apply the Remainder and Factor Theorems Divide 247 / / 8.

Real Zeros of Polynomial Functions. Quick Review.

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.

Real Zeros of Polynomial Functions 2-3. Descarte’s Rule of Signs Suppose that f(x) is a polynomial and the constant term is not zero ◦The number of positive.

Polynomials Integrated Math 4 Mrs. Tyrpak. Definition.

1 Warm-up Determine if the following are polynomial functions in one variable. If yes, find the LC and degree Given the following polynomial function,

Section 5.5 The Real Zeros of a Polynomial Function.

2.4/2.52.4/2.5 Real Zeros of Polynomial Functions.

Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.

3.6 Day 2 Why Synthetic Division? What use is this method, besides the obvious saving of time and paper?

The Remainder Theorem A-APR 2 Explain how to solve a polynomial by factoring.

Using theorems to factor polynomials.  If a polynomial f(x) is divided by x-k, then the remainder r = f(k)  This is saying, when you divide (using synthetic.

If a polynomial f(x) is divided by (x-a), the remainder (a constant) is the value of the function when x is equal to a, i.e. f(a). Therefore, we can use.

Polynomials.  Sample test questions over this material:  Perform the following operation. Express your answer in most simple form.  Write an expression.

Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.

FACTOR to SOLVE 1. X 2 – 4x X 2 – 17x + 52 (x-10)(x + 6) x = 10, -6 (x-4)(x - 13) x = 4,13.

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

3.3 Polynomial and Synthetic Division. Long Division: Let’s Recall.

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

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

Real Zeros of Polynomials Section 2.4. Review – Long Division 1. What do I multiply by to get the first term? 2. Multiply through 3. Subtract 4. Bring.

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 Theorems About Roots of Polynomial Equations

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.

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

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.

Dividing Polynomials Section 4.3.

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.

Divide by x - 1 Synthetic Division: a much faster way!

Descartes Rule of Signs Positive real zeros = Negative real zeros =

5.8 Rational Zero Theorem.

Real Zeros Intro - Chapter 4.2.

4.2 Real Zeros Finding the real zeros of a polynomial f(x) is the same as solving the related polynomial equation, f(x) = 0. Zero, solution, root.

5-5 Theorems About Roots of Polynomial Equations

5.6 Find The Rational Zeros

Rational Root Theorem Math 3 MM3A1.

Finding polynomial roots

Warm Up #2 Factor completely. 2. 2x2 – 5x – 3 1. x2 – x – 12

Notes 5.6 (Day 1) Find Rational Zeros.

Apply the Remainder and Factor Theorems

Real Zeros of Polynomial Functions

Factor Theorems.

Zeros of a Polynomial Function

Remainder and Factor Theorem

Apply the Fundamental Theorem of Algebra

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

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

Notes Over 6.6 Possible Zeros Factors of the constant

8-5 Rational Zero Theorem

Section 2.4: Real Zeros of Polynomial Functions

& AM3.1d To Use The Rational Roots Theorem & Synthetic Division

The Real Zeros of a Polynomial Function

Dividing Polynomials (SYNTHETIC Division)

Presentation transcript:

2.5 Zeros of Polynomial Functions The Rational Zero Theorem Possible rational zeros = Provides us with a list of all possible rational zeros of a polynomial function. Factors of the constant Factors of the l.c. 1

List all possible rational zeros of f(x) = x3 + 3x2 – 6x – 8 Example List all possible rational zeros of f(x) = x3 + 3x2 – 6x – 8 You try one List all possible rational zeros of f(x) = x3 + 2x2 – 5x – 6 2

List all possible rational zeros of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8 Example List all possible rational zeros of f(x) = 3x4 – 11x3 – 3x2 – 6x + 8 You try one List all possible rational zeros of f(x) = 4x5 + 12x4 –x – 3 3

Combining the list with synthetic division will allow us to solve a function. Example Find all zeros of f(x) = x3 – 2x2 – 11x + 12 4

You try one Find all zeros of f(x) = x3 + 8x2 + 11x – 20 5

P. 335 #1 – 15 odd 6