Section 5.9 Solving Equations by Factoring

Jul 03, 2012

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Section 5.9 Solving Equations by Factoring

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1. Section 5.9Solving Equations by Factoring Solutions to Equations in One Variable: Where the curve crosses the x-Axis (if it does!) Solving Quadratic Equations ax2 + bx + c = 0 Zero factor property Solving Higher Degree Equations Problem Solving

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. Solving Quadratic Equations by Factoring. The quadratic equation is written in the form ax 2 + bx + c = 0 To solve quadratic equations by factoring we use the Zero Product Principle If A  B = 0 then A = 0 or B = 0

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Solving Equations by Factoring

Solving Equations by Factoring. Solving Equations.

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6.3 Solving Quadratic Equations by Factoring

6.3 Solving Quadratic Equations by Factoring. 1. Terminology. 2. Zero Factor Theorem. 3. Methods for Solving. Terms. Zero Factor Theorem. If p and q are algebraic expressions, then pq =0 if and only if p=0 or q=0 Example: (x+2)(2X-4)=0; x+2=0 and/or 2x-4=0 Steps

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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. Chapter 10 Lesson 10-5. Introduction.

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Factoring and Solving Polynomial Equations Section 6.4

Factoring and Solving Polynomial Equations Section 6.4. Special Factoring Patterns. Sum of two cubes a 3 + b 3 = (a + b) (a 2 − ab + b 2 ) x 3 + 8 = (x + 2) (x 2 − 2x + 4) Difference of two cubes a 3 − b 3 = (a − b) (a 2 + ab + b 2 ) 8x 3 − 1 = (2x − 1) (4x 2 + 2x + 1).

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1.3 Solving Quadratic Equations by Factoring

1.3 Solving Quadratic Equations by Factoring. (p. 18) How can factoring be used to solve quadratic equation when a=1?. Vocabulary Reminder. Monomial Binomial Trinomial. An expression that is either a number, a variable, or the product of a number and one or more variables. (4, x, 5y).

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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. Zero Product Property. For any real numbers a and b , if ab =0, then either a =0, b =0, or both. In this first example, the equation is already factored and is set equal to zero. To solve, simply set the individual factors equal to zero.

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5.5 Solving Quadratic Equations by Factoring

5.5 Solving Quadratic Equations by Factoring. The form ax 2 + bx + c = 0 is the standard form of a quadratic equation. For example, and are all quadratic equations, but only x 2 + 5 x +6 = 0 is in standard form. Solving Quadratic Equations by Factoring. Quadratic Equation

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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. X- Box. Product a∙c. factors. factors. Sum b. X-box Factoring. This is a guaranteed method for factoring quadratic equations—no guessing necessary! We will learn how to factor quadratic equations using the x-box method

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5.8 Polynomial Equations - Solving Equations by Factoring

5.8 Polynomial Equations - Solving Equations by Factoring. Solutions to Equations in One Variable: Where the curve crosses the x-Axis (if it does!) Solving Quadratic Equations ax 2 + bx + c = 0 Zero factor property Solving Higher Degree Equations Problem Solving

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9.8 Solving Equations by Factoring

9.8 Solving Equations by Factoring. Objectives: Find the zeros of a function. Solve equations by factoring. Standard Addressed: 2.8.11.N. Solve quadratic equations. Ex. 2 Find the zeros of the polynomial function y = . (x + 9) (x + 2) x + 9 = 0 x = -9 x + 2 = 0 x = -2. Ex. 3a .

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Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring. 1. Terminology. 2. Zero Factor Theorem. 3. Methods for Solving. Terms. Zero Factor Theorem. If p and q are algebraic expressions, then pq =0 if and only if p=0 or q=0 Example: (x+2)(2X-4)=0; x+2=0 and/or 2x-4=0 Steps

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11.6 – Solving Quadratic Equations by Factoring

11.6 – Solving Quadratic Equations by Factoring. A quadratic equation is written in the Standard Form ,. where a , b , and c are real numbers and . Examples:. (standard form). 11.6 – Solving Quadratic Equations by Factoring. Zero Factor Property:.

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Solving Polynomial Equations by Factoring

Solving Polynomial Equations by Factoring. Quick Review. FACTORING a polynomial means to break it apart into its prime factors. For example: x 2 – 4 = ( x + 2)( x – 2) x 2 + 6 x + 5 = ( x + 1)( x + 5) 3 y 2 + 10 y – 8 = (3 y – 2)( y + 4).

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5.2: Solving Quadratic Equations by Factoring

5.2: Solving Quadratic Equations by Factoring. (p. 256). To solve a quadratic eqn. by factoring, you must remember your factoring patterns !. Zero Product Property. Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 or B=0.

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6.3 Solving Quadratic Equations by Factoring

6.3 Solving Quadratic Equations by Factoring. Write a quadratic equation with given roots. Roots or Zeros of the Quadratic Equation. The Roots or Zeros of the Quadratic Equation are the points where the graph hits the x axis.

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F-2 Solving Equations by Factoring

F-2 Solving Equations by Factoring. N#_____ _____/_____/_____. E1 Solve 8b 2 – 40b = 0. E2 Solve x 2 = –10x. E3 Solve x 2 + 2x – 15 = 0. E4 Solve 3x 2 + 2x – 16 = 0. E5 Solve. E6 Solve. Ex 7 Solve. 18x 3 – 8x = 0. Ex 8 Solve. 4x 2 + 36x + 81=0.

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Solving Quadratic Equations By Factoring

Solving Quadratic Equations By Factoring. Chapter 5 Section 2. Factoring. 1. 2. 3. Factoring. 4. 5. Factoring. 6. 7. Solving Quadratic Equations Using Factoring. Steps: Factor the Equation Set equations equal to 0 Solve for x. Example. Example. 2.). CLASSWORK.

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5.2: Solving Quadratic Equations by Factoring

5.2: Solving Quadratic Equations by Factoring. (p. 256) How do you factor: x 2 +bx +c ax 2 +bx+c a 2 −b 2 a 2 +2ab +b 2 a 2 −2ab +b 2 How do you solve a quadratic function?. Everything you ever learned about factoring in one section!.

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Solving Equations by Factoring

Solving Equations by Factoring. Standard Form Quadratic Equation. Quadratic equations can be written in the form ax 2 + bx + c = 0 where a , b , and c are real numbers with a  0. Standard form for a quadratic equation is in descending order equal to zero. BACK.

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Solving Equations by factoring

Solving Equations by factoring. Algebra I Mrs. Stoltzfus. Consider this…. If 4a = 0, what do you know?. We know that a = 0, because of the multiplication property of 0. Consider this…. What if ab = 0? What do you know?. This tells us that a = 0 or b = 0!.

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Solving Quadratic Equations by Factoring

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