Basic Factoring of Polynomials

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Basic Factoring of Polynomials
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Three steps to solving quadratic polynomials Solve by factoring Solve by using the square root property Solve by using the quadratic equation

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

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

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.

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

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

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

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

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

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

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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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