Transcript 9.6 Factoring Review

9.6 Perfect Squares &
Factoring
Perfect Square Trinomials
First term must be a perfect square
 Last term must be a perfect square
 Middle term must equal 2(first term)(last
term)
 Then, a2+2ab+b2=(a+b)2
 and a2-2ab+b2=(a+b)2

Determine whether
is a perfect square
trinomial. If so, factor it.
Yes,
1. Is the first term a perfect square?
2. Is the last term a perfect square?
3. Is the middle term equal to
Answer:
Yes,
? Yes,
is a perfect square trinomial.
Write as
Factor using the pattern.
Determine whether
square trinomial. If so, factor it.
1. Is the first term a perfect square?
2. Is the last term a perfect square?
3. Is the middle term equal to
Answer:
is a perfect
Yes,
Yes,
? No,
is not a perfect square trinomial.
Determine whether each trinomial is a perfect square
trinomial. If so, factor it.
a.
Answer: not a perfect square trinomial
b.
Answer: yes;
Factor
.
First check for a GCF. Then, since the polynomial has two
terms, check for the difference of squares.
6 is the GCF.
and
Answer:
Factor the difference
of squares.
Factor
.
This polynomial has three terms that have a GCF of 1.
While the first term is a perfect square,
the last term is not. Therefore, this is not a perfect
square trinomial.
This trinomial is in the form
Are there two
numbers m and n whose product is
and whose sum is 8? Yes, the product of 20 and –12 is
–240 and their sum is 8.
Write the pattern.
and
Group terms with
common factors.
Factor out the GCF
from each grouping.
Answer:
is the
common factor.
Factor each polynomial.
a.
Answer:
b.
Answer:
Solving Perfect Square
Trinomials
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
solution in the original equation.
Solve
Answer:
Solve
.
Original equation
Square Root Property
Add 7 to each side.
or
Separate into two equations.
Simplify.
Answer: The solution set is
Check each
solution in the original equation.
Solve
.
Original equation
Recognize perfect
square trinomial.
Factor perfect
square trinomial.
Square Root Property
Subtract 6 from each side.
or
Separate into two equations.
Simplify.
Answer: The solution set is
Check this
solution in the original equation.
Solve
.
Original equation
Square Root Property
Subtract 9 from each side.
Answer: Since 8 is not a perfect square, the solution set is
Using a calculator, the approximate
solutions are
or about –6.17 and
or about –11.83.
Check You can check your answer using a graphing
calculator. Graph
and
Using the
INTERSECT feature of your graphing calculator, find
where
The check of –6.17 as one of the
approximate solutions is shown.
Solve each equation. Check your solutions.
a.
Answer:
b
Answer:
c.
Answer: