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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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**Quadratic Polynomials**

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

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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 z2 + 4z + 4 z2 + 4z + 4 = 0

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**Quadratic factoring (Cont.)**

The first term is z2 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 ) ( F L ) The F * F must equal the first term. The L * L must equal the last term.

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**Quadratic factoring (Cont.)**

The inner plus the outer must equal the middle term. z * z = z2 First Term 2z + 2z = 4z Middle Term 2 * 2 = 4 Last Term

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**Quadratic factoring (Cont.)**

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

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**Example Factor: x2 + x – 6 First: (x )(x ) Second: 3 * (-2) = -6**

3x - 2x = x Third: Answer: (x + 3)(x - 2)

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Quadratic Equation A quadratic function can also be solved by the quadratic formula: It must be in standard form: Ax2 + Bx + C = 0

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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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**Some polynomials can be grouped to factor the like terms.**

By Factoring Some polynomials can be grouped to factor the like terms. x3 + 2x2 + 2x + 4 = 0 Example: First: Group the terms (x3 + 2x2) + (2x + 4) = 0 Second: Factor out common terms x2 (x + 2) + 2 (x + 2) = 0 Third: Factor the (x + 2) term Answer: (x2 + 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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**Tutorial Services – The Math Center**

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

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**Links and Handouts Working with Polynomials Worksheet**

Factoring Polynomials Handout Completing the Square Handout Algebra and Logarithmic Functions Handout Polynomial Quiz Working with Polynomials Quiz

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7-3 Solving Equations Using Quadratic Techniques

7-3 Solving Equations Using Quadratic Techniques

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