Presentation is loading. Please wait.

Presentation is loading. Please wait.

Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:

Published byHarry Sutton Modified over 9 years ago

Similar presentations

Presentation on theme: "Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:"— Presentation transcript:

1 Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:

2 Variable substitution Another method of solving higher-degree polynomial equations involves recognizing polynomials that have quadratic form. Ex. 2. Solve

3 The Rational Root Theorem Let P(x) be a polynomial of degree n with integral coefficients and a nonzero constant term: If one of the roots of the equation P(x) = 0 is where P and q are nonzero integers with no common factor other than 1, then p must be a factor of and q must be a factor of

4 Ex. 3. a. According to the rational root theorem, what are the possible rational roots of is a possible rational root if p is a factor of –4 and q is a factor of 3.

5 b. Determine whether any of the possible rational roots really are roots. Then find all other roots, real or imaginary. Try synthetic substitution Or substitute in to see if any P(x) = 0 Use synthetic division

6 Find the other roots of Check x = -2 again because it may be a double root

Download ppt "Solving Polynomial Equations by Factoring Factoring by grouping Ex. 1. Solve:"

Similar presentations

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem

Lesson 3.4 – Zeros of Polynomial Functions Rational Zero Theorem
4.4 Rational Root Theorem.

4.4 Rational Root Theorem.
Rational Root Theorem.

Rational Root Theorem.
Lesson 2.6 Pre-Calc Part 2 When trying to ‘factor’ a quadratic into two binomials, we only ever concern ourselves with the factors of the ‘a’ --- leading.

Lesson 2.6 Pre-Calc Part 2 When trying to ‘factor’ a quadratic into two binomials, we only ever concern ourselves with the factors of the ‘a’ --- leading.
Zeros of Polynomial Functions Section 2.5. Objectives Use the Factor Theorem to show that x-c is a factor a polynomial. Find all real zeros of a polynomial.

Zeros of Polynomial Functions Section 2.5. Objectives Use the Factor Theorem to show that x-c is a factor a polynomial. Find all real zeros of a polynomial.
Introduction You have learned several methods for solving polynomial equations by determining the factors, but not all equations are factorable. In this.

Introduction You have learned several methods for solving polynomial equations by determining the factors, but not all equations are factorable. In this.
4.4 Notes The Rational Root Theorem. 4.4 Notes To solve a polynomial equation, begin by getting the equation in standard form set equal to zero. Then.

4.4 Notes The Rational Root Theorem. 4.4 Notes To solve a polynomial equation, begin by getting the equation in standard form set equal to zero. Then.
Warm-up Find all the solutions over the complex numbers for this polynomial: f(x) = x4 – 2x3 + 5x2 – 8x + 4.

Warm-up Find all the solutions over the complex numbers for this polynomial: f(x) = x4 – 2x3 + 5x2 – 8x + 4.
Rational Root Theorem. Finding Zeros of a Polynomial Function Use the Rational Zero Theorem to find all possible rational zeros. Use Synthetic Division.

Rational Root Theorem. Finding Zeros of a Polynomial Function Use the Rational Zero Theorem to find all possible rational zeros. Use Synthetic Division.
Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!

Solving Polynomial Equations. Fundamental Theorem of Algebra Every polynomial equation of degree n has n roots!
Chapter 4 – Polynomials and Rational Functions

Chapter 4 – Polynomials and Rational Functions
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.)

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.)
Zeros of Polynomials PolynomialType of Coefficient 5x 3 + 3x 2 + (2 + 4i) + icomplex 5x 3 + 3x 2 + √2x – πreal 5x 3 + 3x 2 + ½ x – ⅜rational 5x 3 + 3x.

Zeros of Polynomials PolynomialType of Coefficient 5x 3 + 3x 2 + (2 + 4i) + icomplex 5x 3 + 3x 2 + √2x – πreal 5x 3 + 3x 2 + ½ x – ⅜rational 5x 3 + 3x.
The Rational Zero Theorem The Rational Zero Theorem gives a list of possible rational zeros of a polynomial function. Equivalently, the theorem gives all.

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

2.3 Synthetic Substitution
9.9 The Fundamental Theorem of Algebra

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

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

Factor Theorem & Rational Root Theorem
The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.

The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.
Roots & Zeros of Polynomials III

Roots & Zeros of Polynomials III

Similar presentations

Ads by Google