9­6 perfect square trinomials
March 07, 2013
Take out last nights homework 9-5 front
and back...we will go over the answers
Title: Perfect Squares and Factoring
EQ: How do we factor perfect square trinomials? How do we s0lve perfect square trinomials?
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9­6 perfect square trinomials
March 07, 2013
My example:
Notes
• The first term and the last term must be perfect squares.
• The middle term must be 2 times the square root of “a” multiplied by the square root of “c” with the same variable.
• So if you see this a +2ab+b then factored it is (a+b)
• Or if you see this a ­2ab+b then factored it is (a­
b)
• 4x +20x +25
• Is the first term a perfect square?
• Is the last term a perfect square?
• Is the middle term 2* (2+5)?
Then it works. Factored form:
(2x+5)(2x+5)
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Another example:
Third example
16x +32x+64
• Is the first term a perfect square?
• Is the last term a perfect square?
• Is the middle term 2*(4+8) ?
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•
•
•
•
•
9y ­12y+4
Is the first term a perfect square?
Is the last term a perfect square?
Is the middle term 2* (3+2)?
Then it works. Factored form
(3y­2)(3y­2)
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9­6 perfect square trinomials
Determine whether each trinomial is a perfect square trinomial. If so, factor it.
a.
Answer: not a perfect square trinomial
b.
March 07, 2013
If the factors are not perfect squares
• Then look to see if you can take out a GCF.
• THEN look for difference of squares or a perfect square trinomial.
• If it is NOT either of those then look to see if you can factor the trinomial (a*c)/a to equal b (sections 9­3 and 9­4)
Answer: yes; Mar 7­11:57 AM
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Factor .
Factor .
6 is the GCF.
Answe
Factor the difference of squares.
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9­6 perfect square trinomials
March 07, 2013
Factor each polynomial.
a.
Write the pattern.
and
Group terms with common factors.
b.Answer:
Answer:
Factor out the GCF from each grouping.
Answe
is the
common factor.
Example 6­2a
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9-6 skills practice 1st column
only!
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Solve
Original equation
Recognize
as a perfect square trinomial.
Factor the perfect square trinomial.
Set the repeated factor equal to zero.
Solve for x.
Answer: Thus, the solution set is
Check this Example 6­3a
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9­6 perfect square trinomials
March 07, 2013
Another type of problem
Solve
• Using the square root to solve equations.
• Take the square root of both sides. Solve for the variable.
• Can be done after realizing that the polynomial is a perfect square trinomial and factoring that.
Answer:
Example 6­3b
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Examples of square root property
Example:
• (a+2) =49
Solve .
Original equation
Square Root Property
Example:
y ­4y+4=25
or
Add 7 to each Separate into two equations.
side.
Simplify.
Answer: The solution set is Check each Example 6­4a
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9­6 perfect square trinomials
March 07, 2013
Solve .
or
Original equation
Separate into two equations.
Simplify.
Recognize perfect square trinomial.
Answer: The solution set is Check this Factor perfect square trinomial.
Square Root Property
Subtract 6 from each side.
Example 6­4a
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Example 6­4a
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Solve .
Original equation
Square Root Property
Subtract 9 from each Answer: Since 8 is not a perfect square, side.
the solution set is
Using a calculator, the approximate
solutions are or about –6.17 and
Check You can check your answer using and
a graphing calculator. Graph
Using the INTERSECT feature of your The graphing calculator, find where
check of –6.17 as one of the approximate solutions is shown. Example 6­4a
Example 6­4a
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9­6 perfect square trinomials
March 07, 2013
Practice/HW
• P.512 #17­41 odd
• P.513 #43­55 odd
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