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Basic Factoring of Polynomials Brought to you by Tutorial Services – The Math Center.

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Presentation on theme: "Basic Factoring of Polynomials Brought to you by Tutorial Services – The Math Center."— Presentation transcript:

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2 Basic Factoring of Polynomials Brought to you by Tutorial Services – The Math Center

3 Solving Quadratic Polynomials Three steps to solving quadratic polynomials  Solve by factoring  Solve by using the square root property  Solve by using the quadratic equation

4 How does one isolate ‘x’ in a case like the following? It is unnecessarily difficult. Therefore, other methods must be used. Quadratic Polynomials

5 Quadratic factoring Example: First we need to…  MAKE THE EQUATION EQUAL TO ZERO  So: This polynomial can be factored by considering the following:  The polynomial has three terms  First, Middle, and Last z 2 + 4z + 4 z 2 + 4z + 4 = 0

6 The first term is z 2 The Middle term is 4z The Last terms is 4 To factor, the best way to start is to place the parenthesis for factoring: ( F L )  The F * F must equal the first term.  The L * L must equal the last term. Quadratic factoring (Cont.)

7 The inner plus the outer must equal the middle term. Quadratic factoring (Cont.) z * z = z 2  First Term  2z + 2z = 4z  Middle Term  2 * 2 = 4  Last Term

8 In summary: ( F L ) F * F = First term L * L = Last Term Inner + Outer = Middle Term Quadratic factoring (Cont.)

9 Example x 2 + x – 6Factor: (x )(x)First: Second:3 * (-2) = -6 3x - 2x = x Third: Answer: (x + 3)(x - 2)

10 A quadratic function can also be solved by the quadratic formula: It must be in standard form: Ax 2 + Bx + C = 0 Quadratic Equation

11 Cubic Polynomials These polynomials can be solved by using the synthetic division or if possible, by factoring. Only factoring will be considered

12 By Factoring Some polynomials can be grouped to factor the like terms. x 3 + 2x 2 + 2x + 4 = 0Example: First: Group the terms (x 3 + 2x 2 ) + (2x + 4) = 0 Second: Factor out common terms x 2 (x + 2) + 2 (x + 2) = 0 Third: Factor the (x + 2) term Answer: (x 2 + 2)(x + 2) = 0

13 SUMMARY  Polynomials can be of various degrees; the most popular are: Linear Quadratic Cubic Factoring is a tool to help solve for a variable. In order to solve by factoring it is necessary to MAKE THE EQUATION EQUAL TO ZERO.

14 Questions? Brought to you by Tutorial Services – The Math Center

15 Links and Handouts Working with Polynomials Worksheet Factoring Polynomials Handout Completing the Square Handout Algebra and Logarithmic Functions Handout Algebra and Logarithmic Functions Handout Polynomial Quiz Working with Polynomials Quiz


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