basic factoring of polynomials brought to you by tutorial services – the math center
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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.
0442 xx
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
z2 + 4z + 4
z2 + 4z + 4 = 0
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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.)
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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
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In summary:
( F L ) ( F L )
F * F = First term L * L = Last Term Inner + Outer = Middle Term
Quadratic factoring (Cont.)
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Examplex2 + 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:
Ax2 + Bx + C = 0
Quadratic Equation
a
acbb
2
)4)(( 2
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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
0422 23 xxx
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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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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 Polynomial Quiz Working with Polynomials Quiz