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

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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

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

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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

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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.)

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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

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

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

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

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

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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

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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.

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

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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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