Download File

WARM UP
• Write down objective and homework in agenda.
• Lay out homework (Faceing Equations
worksheet)
• Homework (Factor a=1 worksheet)
Warm Up
• Math 8 benchmark
Vocabulary!
• Factoring trinomials: Find the binomial
factors of trinomials
Teach me how to factor…
• http://www.youtube.com/watch?v=OFSrINhf
NsQ
Review: (y + 2)(y + 4)
First terms: y2
Outer terms: +4y
Inner terms: +2y
Last terms: +8
Combine like terms.
y2 + 6y + 8
y
+2
y2
+2y
+4 +4y
+8
y
In this lesson, we will begin with y2 + 6y + 8 as our
problem and finish with (y + 2)(y + 4) as our answer.
Here we go! 1) Factor y2 + 6y + 8
Do we have a GCF? Nope!
Now we will learn Trinomials! You will set up a
table with the following information.
Product of the first and last
coefficients
Middle
coefficient
The goal is to find two factors in the first column that
add up to the middle term in the second column.
We’ll work it out in the next few slides.
M
A
1) Factor y2 + 6y + 8
Create your MAMA table.
Product of the
first and last
coefficients
Multiply
+8
Add
+6
Middle
coefficient
Here’s your task…
What numbers multiply to +8 and add to
+6? If you cannot figure it out right away,
write the combinations.
1) Factor y2 + 6y + 8
Place the factors in the table.
Multiply
+8
Which has
a sum
of +6?
+1, +8
-1, -8
+2, +4
-2, -4
Add
+6
+9, NO
-9, NO
+6, YES!!
-6, NO
We are going to use these numbers in the next step!
1) Factor
Multiply
+8
+2, +4
2
y
+ 6y + 8
Add
+6
+6, YES!!
Hang with me now! Replace the middle number of
the trinomial with our working numbers from the
MAMA table
y2 + 6y + 8
y2 + 2y + 4y + 8
Now, group the first two terms and the last two
terms.
We have two groups!
(y2 + 2y)(+4y + 8)
Almost done! Find the GCF of each group and factor it
out.
If things are done
right, the
y(y + 2) +4(y + 2)
parentheses should
Factor out the
GCF’s. Write them
in their own group.
be the same.
(y + 4)(y + 2)
Tadaaa! There’s your answer…(y + 4)(y + 2)
You can check it by multiplying.
M
A
2) Factor x2 – 2x – 63
Create your MAMA table.
Product of the
first and last
coefficients
Signs need to
be different
since number
is negative.
Multiply
-63
-63, 1
-1, 63
-21, 3
-3, 21
-9, 7
-7, 9
Add
-2
-62
62
-18
18
-2
2
Middle
coefficient
Replace the middle term with our working
numbers.
x2 – 2x – 63
x2 – 9x + 7x – 63
Group the terms.
(x2 – 9x) (+ 7x – 63)
Factor out the GCF
x(x – 9) +7(x – 9)
The parentheses are the same!!
(x + 7)(x – 9)
Here are some hints to help
you choose your factors in the
MAMA table.
1) When the last term is positive, the factors
will have the same sign as the middle term.
2) When the last term is negative, the factors
will have different signs.
2) Factor 2x2 - 14x + 12
Find the GCF!
2(x2 – 7x + 6)
Now do the MAMA table!
Signs need to
be the same as
the middle
sign since the
product is
positive.
Multiply
+6
Add
-7
-1, -6
-7
-2, -3
-5
Replace the middle term.
2[x2 – x – 6x + 6]
Group the terms.
2[(x2 – x)(– 6x + 6)]
Factor out the GCF
2[x(x – 1) -6(x – 1)]
The parentheses are the same!
2(x – 6)(x – 1)
Don’t forget to always look for a GCF first!!
More Examples!
• http://www.regentsprep.org/Regents/math/A
LGEBRA/AV6/PracFact2.htm
Factor x2 + 3x + 2
1.
2.
3.
4.
(x + 2)(x + 1)
(x – 2)(x + 1)
(x + 2)(x – 1)
(x – 2)(x – 1)
You Try!!!
• 1) (x+4)(x+25)
• 2) (x−9)(x+3)
You Try!!!
• 3) (x+4)(x+4)
• 4) (x− 5)(x− 4)
You Try!
• 5) (a+ 4b)(a+ 12b)
• 6) (a− 25)(a+ 1)
More Practice!
• http://www.quia.com/jg/678595.html
• http://www.quia.com/jg/678595.html
• http://hotmath.com/help/gt/genericalg1/secti
on_6_10.html
Extra Resources
• http://www.phschool.com/webcodes10/index.cfm?fus
eaction=home.gotoWebCode&wcprefix=ata&wcsuffix=
0905
• http://www.phschool.com/atschool/academy123/engli
sh/academy123_content/wl-book-demo/ph-275s.html
• http://teachers.henrico.k12.va.us/math/hcpsalgebra1/
Documents/examviewweb/ev8-4.htm
• http://www.regentsprep.org/Regents/math/ALGEBRA/
AV6/indexAV6.htm
• http://www.regentsprep.org/Regents/math/ALGEBRA/
AV6/PracFact2.htm