Presentation is loading. Please wait.

Presentation is loading. Please wait.

Factoring a Polynomial. Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 Use the graph or table to find at least one real root.

Published byTrevor Parker Modified over 9 years ago

Similar presentations

Presentation on theme: "Factoring a Polynomial. Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 Use the graph or table to find at least one real root."— Presentation transcript:

1 Factoring a Polynomial

2 Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 Use the graph or table to find at least one real root. x = -4 is a real root because it is an x-intercept. Since x = -4 is a root, (x + 4) is a factor of the original cubic equation. Now use polynomial division to “factor out” the (x + 4).

3 Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 x 3 + 2x 2 – 11x – 12 x + 4 x2x2 x3x3 4x24x2 -2x 2 -2x -8x -3x -3 -12 Now we can rewrite the cubic: Since the graph of the cubic had more than one real root, this may be able to be factored more. This quadratic can be factored using old techniques: (x + 1)(x – 3) Thus, the completely factored form is:

4 Let’s try another example.

5 Example 2: Factoring a Polynomial Completely factor x 4 – x 3 + 4x – 16 Use the graph or table to find at least one real root. x = -2 is a real root because it is an x-intercept. Since x = -2 is a root, (x + 2) is a factor of the original degree 4 equation. Now use polynomial division to “factor out” the (x + 2).

6 Example 2: Factoring a Polynomial x 4 – x 3 + 0x 2 + 4x – 16 x + 2 x3x3 x4x4 2x32x3 -3x 3 -3x 2 -6x 2 6x26x2 6x6x 12x -8x -8 Completely factor x 4 – x 3 + 4x – 16 -16 Now we can rewrite the degree 4 equation: Make sure to include all powers of x Since the graph of the degree 4 equation had more than one real root, this may be able to be factored more. Let’s check the graph of this cubic to see if it has a real root.

7 Example 2: Factoring a Polynomial Completely factor x 4 – x 3 + 4x – 16 Current Factored form: Use the graph or table of the cubic in the factored form to find at least one real root. x = 2 is a real root because it is an x-intercept. Since x = 2 is a root, (x – 2) is a factor of the cubic in the factored form. Now use polynomial division to “factor out” the (x – 2) of the cubic in the factored form.

8 Example 2: Factoring a Polynomial x 3 – 3x 2 + 6x – 8 x – 2 x2x2 x3x3 -2x 2 -x2-x2 -x-x 2x2x 4x4x 4 -8 Now we can rewrite the current factored form as: Since the graph of the cubic had only one real root, this may NOT be able to be factored more. This quadratic can NOT be factored using old techniques (No x-intercepts). Thus, the completely factored form is: Current Factored form: Completely factor x 4 – x 3 + 4x – 16

Download ppt "Factoring a Polynomial. Example 1: Factoring a Polynomial Completely factor x 3 + 2x 2 – 11x – 12 Use the graph or table to find at least one real root."

Similar presentations

6.4 Solving Polynomial Equations

6.4 Solving Polynomial Equations
Creating Polynomials Given the Zeros.. What do we already know about polynomial functions? They are either ODD functions They are either EVEN functions.

Creating Polynomials Given the Zeros.. What do we already know about polynomial functions? They are either ODD functions They are either EVEN functions.
Factors, Roots, and zeroes

Factors, Roots, and zeroes
Finding the Roots of a Polynomial. 2 Real Roots and 2 Complex Roots because it only has 2 x-intercepts but has 4 “turns” Classifying the Roots of a Polynomial.

Finding the Roots of a Polynomial. 2 Real Roots and 2 Complex Roots because it only has 2 x-intercepts but has 4 “turns” Classifying the Roots of a Polynomial.
Solving Quadratic Equations Tammy Wallace Varina High.

Solving Quadratic Equations Tammy Wallace Varina High.
Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x 2 + 55 =

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =
7.1 – Completing the Square

7.1 – Completing the Square
Roots & Zeros of Polynomials I How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related.

Roots & Zeros of Polynomials I How the roots, solutions, zeros, x-intercepts and factors of a polynomial function are related.
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.
Solution of Polynomial Equations

Solution of Polynomial Equations
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!
Solving Quadratic (and polynomial) Equations by Factoring.

Solving Quadratic (and polynomial) Equations by Factoring.
The Rational Zero Theorem

The Rational Zero Theorem
Solving Quadratic Equations by the Quadratic Formula

Solving Quadratic Equations by the Quadratic Formula
6.8 Analyzing Graphs of Polynomial Functions. Zeros, Factors, Solutions, and Intercepts. Let be a polynomial function. The following statements are equivalent:

6.8 Analyzing Graphs of Polynomial Functions. Zeros, Factors, Solutions, and Intercepts. Let be a polynomial function. The following statements are equivalent:
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.
Bell Ringer 1. What is the Rational Root Theorem (search your notebook…Unit 2). 2. What is the Fundamental Theorem of Algebra (search your notebook…Unit.

Bell Ringer 1. What is the Rational Root Theorem (search your notebook…Unit 2). 2. What is the Fundamental Theorem of Algebra (search your notebook…Unit.
Additional Mathematics for the OCR syllabus - Algebra 8

Additional Mathematics for the OCR syllabus - Algebra 8
Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)

Do Now: Factor x2 – 196 4x2 + 38x x2 – 36 (x + 14)(x – 14)
Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n≥1, then the equation f(x) = 0 has at least one complex root. Date: 2.6 Topic:

Fundamental Theorem of Algebra If f(x) is a polynomial of degree n, where n≥1, then the equation f(x) = 0 has at least one complex root. Date: 2.6 Topic:

Similar presentations

Ads by Google