4 3 Solving Quadratic Equations by Factoring Recall
![4. 3 Solving Quadratic Equations by Factoring 4. 3 Solving Quadratic Equations by Factoring](https://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-1.jpg)
4. 3 Solving Quadratic Equations by Factoring
![Recall multiplying these binomials to get the standard form for the equation of a Recall multiplying these binomials to get the standard form for the equation of a](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-2.jpg)
Recall multiplying these binomials to get the standard form for the equation of a quadratic function: (x + 3)(x + 5) = + 5 x +3 x +15 The “reverse” of this process is called factoring. Writing a trinomial as a product of two binomials is called factoring. (x + 3)(x + 5)
![Factor Since the lead coefficient is 1, we need two numbers that multiply to Factor Since the lead coefficient is 1, we need two numbers that multiply to](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-3.jpg)
Factor Since the lead coefficient is 1, we need two numbers that multiply to – 28 and add to – 12. Factors of -28 -1, 28 1, -28 -2, 14 2, -14 -4, 7 4, -7 Sum of Factors -3 Therefore: 27 -27 12 -12 3
![Factor the expression: = (x-3)(x+7) Cannot be factored Factor the expression: = (x-3)(x+7) Cannot be factored](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-4.jpg)
Factor the expression: = (x-3)(x+7) Cannot be factored
![Factoring a Trinomial when the lead coefficient is not 1. Factor: We need a Factoring a Trinomial when the lead coefficient is not 1. Factor: We need a](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-5.jpg)
Factoring a Trinomial when the lead coefficient is not 1. Factor: We need a combination of factors of 3 and 10 that will give a middle term of – 17. Our approach will guess and check. Here are some possible factorizations: This is the factorization we seek.
![Special Factoring Patterns you should remember: Pattern Name Difference of Two Squares Perfect Square Special Factoring Patterns you should remember: Pattern Name Difference of Two Squares Perfect Square](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-6.jpg)
Special Factoring Patterns you should remember: Pattern Name Difference of Two Squares Perfect Square Trinomial Pattern Example
![Factor the quadratic expression: Factor the quadratic expression:](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-7.jpg)
Factor the quadratic expression:
![A monomial is an expression that has only one term. As a first step A monomial is an expression that has only one term. As a first step](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-8.jpg)
A monomial is an expression that has only one term. As a first step to factoring, you should check to see whether the terms have a common monomial factor. Factor:
![You can use factoring to solve certain quadratic equation. A quadratic equation in one You can use factoring to solve certain quadratic equation. A quadratic equation in one](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-9.jpg)
You can use factoring to solve certain quadratic equation. A quadratic equation in one variable can be written in the form where This is called the standard form of the equation: If this equation can be factored then we can use this zero product property. Zero Product Property Let A and B be real number or algebraic expressions. If AB = 0 the either A=0 or B=0
![Solve: So, either (x+6)=0 Or (x – 3)=0 The solutions are – 6 and Solve: So, either (x+6)=0 Or (x – 3)=0 The solutions are – 6 and](http://slidetodoc.com/presentation_image/199fb5ceb2d0229eed21b4a694af8cfb/image-10.jpg)
Solve: So, either (x+6)=0 Or (x – 3)=0 The solutions are – 6 and 3. These solutions are also called zeros of the function Notice the zeros are the x-intercepts of the graph of the function. x = -6 x=3
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