Transcript Notes

9.5
Factoring Trinomials
9.5 – Factoring Trinomials
Goals / “I can…”
Factor trinomials
9.5 – Factoring Trinomials
Remember how to find the factors of a
number.
Try 24
9.5 – Factoring Trinomials
Look at the binomials
(x + 3) (x + 8)
If I multiplied them out.
2
x + 8x + 3x + 8 * 3 =
2
x + 11x + 24
Notice that the middle term is the sum
of 8 and 3 and the last term is the
product of 8 and 3.
9.5 – Factoring Trinomials
Using this we can factor a trinomial. It
is like doing the opposite of FOIL.
9.5 – Factoring Trinomials
a 2 + 13a + 30
What are the factors of 30?
Which factors add up to 13?
Once you find the correct combination,
write the result as two binomials.
(
)(
)
Here we go! 1) Factor y2 + 6y + 8
Use your factoring chart.
Do we have a GCF? Nope!
Is it a Diff. of Squares problem? No way! 3 terms!
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.
1) Factor
2
y
M
A
+ 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
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!
So your answer would be
(x + 2)(x + 4)
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
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.
9.5 – Factoring Trinomials
TRY:
2
a + 8a + 15
Multiply
+15
Add
+8
Factor x2 + 3x + 2
1.
2.
3.
4.
(x + 2)(x + 1)
(x – 2)(x + 1)
(x + 2)(x – 1)
(x – 2)(x – 1)
9.5 – Factoring Trinomials
What happens if the middle term is
negative?
2
x – 11x + 18
What are the factors of 18 that add up
to – 11?
x  6x  8
2
Example :
x
x
-2
 x
x
Factors of +8:
-4


x x  x
O + I = bx ?
1&8
1x + 8x = 9x
2&4
2x + 4x = 6x
-1 & -8
-1x - 8x = -9x
-2 & -4
-2x - 4x = -6x
2
x  6x  8  (x  2)(x  4)
2
Check your answer
by using FOIL
F
O
I
2
L
(x  2)(x  4)  x  4x  2x  8
2
 x  6x  8
9.5 – Factoring Trinomials
TRY:
2
c – 9c + 20
Remember to make your MAMA
Multiply
+20
Add
-9
9.5 – Factoring Trinomials
What happens if the last term is
negative?
2
p + 8p – 20
Now one term will be positive, one will
be negative.
BE CAREFUL!!!
9.5 – Factoring Trinomials
TRY:
2
x – 5x – 24
9.5 – Factoring Trinomials
Factors with two variables.
This is just like the other problems but
both parts will have a variable.
9.5 – Factoring Trinomials
2
2
d + 17dg – 60g