Transcript Factoring Trinomials x2+bx+c

Objective
The student will be able to:
factor trinomials with grouping.
SOL: A.12
Designed by Skip Tyler, Varina High School
AIM: How do we factor trinomials
of the type x2 + bx + c?
•
Do Now:
List all of the factors of the following
numbers:
1. 24
2. 12
3. 54
4. 56
HW Review:
• Regents Review 10 is due tomorrow.
Big Ideas:
• In earlier courses, you learned how to find the
factors of whole numbers like 15.
• Since 3 x 5 = 15; 3 and 5 are factors of 15.
• You can also find the factors of some trinomials
using similar methods
Review: (y + 2)(y + 4)
y2
+4y
+2y
+8
First terms:
Outer terms:
Inner terms:
Last terms:
Combine like terms.
y2 + 6y + 8
In this lesson, we will begin with y2 + 6y + 8 as our
problem and finish with (y + 2)(y + 4) as our answer.
1) Factor
2
y
M
A
+ 6y + 8
Create your MA 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
2
y
+ 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 y2 + 6y + 8
Multiply
+8
Add
+6
+2, +4 +6, YES!!
Hang with me now! Replace the middle number of
the trinomial with our working numbers from the
MAMA table
+2 and +4
(y + 2)(y + 4)
Now, let’s check our work by
FOILing!
(y + 2)(y + 4)
M
A
2) Factor x2 – 2x – 63
Create your MA 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 factors into two binomials:
x2 – 2x – 63
+7 -9
(x + 7)(x – 9)
Here are some hints to help
you choose your factors in the
MA 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.
Factor
1.
2.
3.
4.
(x + 2)(x + 1)
(x – 2)(x + 1)
(x + 2)(x – 1)
(x – 2)(x – 1)
2
x
+ 3x + 2
Classwork:
• During the classwork, please work quickly
and quietly in your group.
• If you have a question, please first ask a
groupmate.
• If no one still knows at that point, please
then ask me.
• The first group to finish will receive HW
passes.
Summary:
• What is the most challenging part of
factoring trinomials?
M
A
2) Factor 5x2 - 17x + 14
Create your MAMA table.
Product of the
first and last
coefficients
Signs need to
be the same as
the middle
sign since the
product is
positive.
Multiply
+70
-1, -70
-2, -35
-7, -10
Add
-17
-71
-37
-17
Replace the middle term.
5x2 – 7x – 10x + 14
Group the terms.
Middle
coefficient
(5x2 – 7x) (– 10x + 14)
Factor out the GCF
x(5x – 7) -2(5x – 7)
The parentheses are the same! Weeedoggie!
(x – 2)(5x – 7)
Hopefully, these will continue to get easier the
more you do them.
Factor
1.
2.
3.
4.
(2x + 10)(x + 1)
(2x + 5)(x + 2)
(2x + 2)(x + 5)
(2x + 1)(x + 10)
2
2x
+ 9x + 10
Factor
1.
2.
3.
4.
2
6y
(6y2 – 15y)(+2y – 5)
(2y – 1)(3y – 5)
(2y + 1)(3y – 5)
(2y – 5)(3y + 1)
– 13y – 5
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! Weeedoggie!
2(x – 6)(x – 1)
Don’t forget to follow your factoring chart when
doing these problems. Always look for a GCF
first!!