10-4 Factoring Special Products
Homework
Any Questions?
Factoring is the reverse process of multiplying polynomials.
You will be given a polynomial and you must figure out what 2 binomials
would be multiplied together to equal it.
Today we are dealing with special cases only…
The three special cases are as follows:
a2 – b2 = (a + b)(a – b)
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
When you factor, you are writing the product that would equal the
polynomial… just like jeopardy, they give you the answer and you
figure out the question.
Stand UP!
When I say go…
Perform 15 dips off the side of your desk.
4
Example 1: Factoring out a Monomial (one term)
Polynomial
Common Factor
Factored Form
3x + 6
3
3(x + 2)
5x2 – 15x
5x
5x(x – 3)
4x2 + 6x + 8
2
2(2x2 + 3x + 4)
Example 2: Binomial Square Patterns
To recognize the difference of two squares, look for coefficients that are
squares and for variables that are raised to the second power
a2 – b2 = ?
(a + b)(a – b)
Factor the following:
A. 4x2 – 25 = ?
B. 25 – 49x2 = ?
Think Square Root…
Answers: A. (2x + 5)(2x – 5)
B. (5 + 7x)(5 – 7x)
To recognize a perfect square trinomial, remember that the first and
last terms must be positive and perfect squares, a 2 and b 2 , and the
middle term must be twice the product of a and b.
Example 3: Trinomial Patterns
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Factor the following using trinomial patterns:
A. x2 – 4x + 4 = ?
B. 16y2 + 24y + 9 = ?
Again think square roots…
Student of the Day
• Sometimes before you factor, you need to
remove a monomial then begin to factor.
Always do this step first so you never
forget!
Example 4: Removing a monomial
2
3 x – 27 =
2
3( x – 9) =
3(x + 3)(x – 3)
Example 5:
Factor the following:
8 – (x + 2)
Distribute the signs
8–x–2
64 – (x + 2)2
8 + (x + 2)
8+x+2
(6 – x) (10 + x)
Cool Photo of the Day
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Practice
Factor out the greatest common
monomial factor
Practice
Factor the expression
Practice
Factor the expression
Practice
Factor the expression
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3.
Practice
Factor the expression
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Practice
Factor the expression
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Practice
Factor the expression
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Practice
Factor the expression
Homework:
Pg 531 #5-27odds