Transcript 8.3 Factoring Quadratic Trinomials by Grouping NOTES

8.3 Factoring Quadratic
Equations
Objective
The student will be able to:
Factor trinomials with grouping.
Solve quadratic equations using
Zero Product Property .
Factoring Chart
This chart will help you to determine
which method of factoring to use.
Type
Number of Terms
1. GCF
2. Grouping
3. Quadratic
Trinomials
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
In this lesson, we will begin with y2 + 6y + 8 as our
problem and finish with (y + 2)(y + 4) as our answer.
Ex1) Factor: y2 + 6y + 8
Use your factoring chart.
Ex 1) Factor
Product of the
first and last
coefficients
Multiply
+8
2
y
M
A
+ 6y + 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.
Ex 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!
M
A
Ex 2) Factor x2 – 2x – 63
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! Weeedoggie!
(x + 7)(x – 9)
4 steps for solving a quadratic equation
1. Set the equation equal to 0.
2. Factor the equation.
3. Set each part equal to 0 and
solve.
4. Check your answer on the
calculator.
Set = 0
Factor
Split/Solve
Check
Ex 3) Solve: – 24a +144 = –
Put it in descending order.
a2 – 24a + 144 = 0
(a – 12)2 = 0
a – 12 = 0
a = 12
{12}
2
a
Set = 0
Factor
Split/Solve
Check
Ex 4) Solve:
3
x
+
2
2x
= 15x
x3 + 2x2 – 15x = 0
Set = 0
2
x(x + 2x – 15) = 0
Factor
Split/Solve
x(x + 5)(x – 3) = 0
Check
x = 0 or x + 5 = 0 or x – 3 = 0
{0, – 5, 3}
8.3 HW PG. 489
#13 – 29 ODDS
(9 PROBLEMS)
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.