Transcript Factoring Trinomials using T chart

I can factor trinomials with
grouping.
Factoring Chart
This chart will help you to determine
which method of factoring to use.
Type
Number of Terms
1. GCF
2. Grouping
3. T-chart
2 or more
4
3
Review: (y + 2)(y + 4)
y2
+4y
+2y
+8
First terms:
Outer terms:
Inner terms:
Last terms:
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
Use your factoring chart.
Do we have a GCF?
Nope!
Do we have four terms? No! 3 terms!
You will set up a table with the following
information.
Product of the first and
last coefficients
Sum of the factors
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.
1) Factor
2
y
M
A
+ 6y + 8
Create your T-Chart
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
T-Chart
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 parentheses
y(y + 2) +4(y + 2)
should be the same.
Factor out the
GCF’s. Write them
in their own group.
(y + 4)(y + 2)
You can check it by multiplying. There is a shortcut
for these problems when the squared term has a
coefficient of 1.
M
A
2) Factor x2 – 2x – 63
Create your T-Chart
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)
(x + 7)(x – 9)
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
Try These
( x-5) (x-2)
{ -25, 2}
Here are some hints to help
you choose your factors in the
T-Chart.
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.
To Solve (x + 7)(x - 9) = 0
Using the Zero Product Property,
you know that either
x + 7 = 0 or x - 9 = 0
Solve each equation.
x = -7 or x = 9
{-7, 9}
M
A
1)Factor 5x2 - 17x + 14
Create your T-Chart.
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 T-Chart!
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 follow your factoring chart when
doing these problems. Always look for a GCF
first!!