Download FACTORING: TRINOMIALS a = 1

FACTORING USING INSPECTION METHOD PART 1
If we have a trinomial in the form ax2 + bx + c, where a = 1
 For the x2 term, the only factors we have would be (x) (x)
 To get the other part of our binomial factors, we have to use
the values of “b” and “c”
 The values have to MULTIPLY to give “c” and ADD to give “b”
Example: Factor x2 – 5x – 24
-24
1
2
3
4
24
12
8
6
We are looking for two numbers that will:
multiply to give -24
add to give -5
(3)(-8)= -24
(3) + (-8) = -5
(x + 3)(x – 8)
We can check this answer by multiplying the two binomials together:
(x + 3)(x – 8) = x2 – 8x + 3x – 24
= x2 – 5x – 24
NOTE: If the terms are in a different order, we can rearrange the equations
Example: 64 – 16a + a2
Now solve……….
can be rewritten as
a2 – 16a + 64
FACTORING USING INSPECTION METHOD PART 2
If you have ax2 + bx + c, with a ≠1
 look for factors that multiply to give (a)(c)
 these factors should add to give “b”
Example: 2x2 + 5x – 18
 look for factors that multiply to give (2)(-18) = -36
 these factors should add to give 5
Step 1: Set up your brackets (the same way for trinomials)
(2x
)(2x
)
Step 2: Find the factors
-36
1
2
3
-4
6
36
18
12
9
6
Step 3: Place values into brackets. (2x – 4) (2x + 9)
* NEW STEP * Factor if necessary or divide by factors of ‘a’.
2x  4 2x  9
(
) (
)
2x(x – 2) or
2
1
If you were able to factor (2x + 9) you would factor it too.
Answer: (x – 2) (2x + 9)
FACTORING: DIFFERENCE OF SQUARES
Step 1: Set up 2 brackets
(
)(
)
Step 2: Take the square root of the first term and put it at the
start of each bracket
Step 3: Take the square root of the second term and put it at
the end of each bracket
Step 4: Make one bracket positive, one bracket negative
Example: x2 – 49
(
) (
)
(x
) (x
)
(x
7) (x 7)
(x + 7) (x – 7)
One more: x2 – 81
How can I check my answer???
PERFECT SQUARE NUMBERS
A square number is a number that you get by multiplying a number by itself.
These numbers can be whole numbers, fractions, decimals, etc
A perfect square number is when you have a whole number that is squared.
You always end up with whole numbers as answers.
The opposite of “squaring a number” is to take the square root of a number.
The square root of a number tells you what number is multiplied by itself.
The following table gives values for the first 20 perfect square numbers:
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Square
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
Square Root
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
FACTORING USING TRIAL AND ERROR METHOD
When using the trial and error method, there are a few critical
steps that must be followed to get your factors.
Step 1: Get the factors of the ax2 term.
Example: 2x2 = (2x) (x)
3x2 = (3x) (x)
4x2 = (4x) (x)
OR (2x) (2x)
Step 2: Get the factors that give “c”
Step 3: Set up your brackets using the factors from step 1 and
step 2.
Step 4: This is the trial and error part… you have to mix and
match until you find the right combination that gives
you the expression you started with.
Example: Factor
Possibilities
2x2 – 5x – 7
( 2x + 1 ) ( x – 7 )
( 2x – 7 ) (x + 1 )
( 2x – 1 ) (x + 7 )
( 2x + 7 ) ( x – 1 )
Obviously the right combination of factors is: