Basic Factoring of

Polynomials

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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

How does one isolate ‘x’ in a case like the following?

It is unnecessarily difficult.

Therefore, other methods must be used.

0442 xx

Quadratic Polynomials

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.

Quadratic factoring (Cont.)

The inner plus the outer must equal the middle term.

outer

rinn z2

z2

)2)(2( zz

Quadratic factoring (Cont.)

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

Quadratic factoring (Cont.)

Examplex2 + x – 6Factor:

(x )(x )First:

Second: 3 * (-2) = -6

3x - 2x = x

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

A quadratic function can also be solved by the quadratic formula:

It must be in standard form:

Ax2 + Bx + C = 0

Quadratic Equation

a

acbb

2

)4)(( 2

Cubic Polynomials

These polynomials can be solved by using the synthetic division or if possible, by factoring.

Only factoring will be considered

0422 23 xxx

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.

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