Download Looking for two numbers that add to column A and Multiply to

A
•
•
•
•
•
•
•
•
Looking for two numbers that add to
column A and Multiply to column B
7
6
8
-3
-5
13
1
-4
B
•
•
•
•
•
•
•
•
12
8
-9
-10
6
30
-2
4
3 and 4
4 and 2
9 and -1
-5 and 2
-3and -2
3 and 10
2 and -1
-2 and -2
Sneak preview
When you transform a function
Inside the parentheses translates left
and right
Outside the parentheses translates up
and down
𝑓 𝑥 = 2𝑥 − 2 and 𝑔 𝑥 =
𝑥 2 +7, find 𝑓 𝑔 𝑥
𝑓 𝑔(𝑥) = 𝑓 𝑥 2 + 7 = 2 𝑥 2 + 7 − 2
=2𝑥 2 + 14 + 2
=2𝑥 2 + 16
2
𝑥
+ 𝑏𝑥 + 𝑐
What adds to the middle and
multiplies to the end?
𝟐
𝒙
+ 𝟕 𝒙 + 𝟏𝟐
(𝑥 +3) (𝑥 +4 )
What adds to the middle and
multiplies to the end?
Difference of Squares
a2 – b2 = (a – b)(a + b) = (a + b)(a – b)
Ex. 1: Factor a2 - 64
• You can use this rule to factor trinomials that can
be written in the form a2 – b2.
a2 – 64 = (a)2 – (8)2
= (a – 8)(a + 8)
Ex. 2: Factor 9x2 – 100y2
• You can use this rule to factor trinomials that can
be written in the form a2 – b2.
9x2 – 100y2 = (3x)2 – (10y)2
= (3x – 10y)(3x + 10y)
a2
– 64 = (a – 8)(a + 8)
9x2 – 100y2 = (3x – 10y)(3x + 10y)
12 21
30𝑥 2
2) Factor
2
18x
-
3
12x .
Find the GCF
6x2
Divide each term by the GCF
18x2 - 12x3 = 6x2( ___
3 - ___
2x )
18 x 2
6x2
12 x 3
6 x2
Check your answer by distributing.
To Complete the Square
x2 + 6x
• Take half of the coefficient of ‘x’
• Square it and add it 9
x2 + 6x + 9 = (x + 3)2
3
Complete the square, and show what the perfect
square is:
x  12 x x  12 x  36
2
2
y  14 y
y  14 y  49
y  10 y
y  10 y  25
2
2
x  5x
2
2
2
25
x  5x 
4
2
x  6
2
 y  7
2
 y  5
2
5

x 
2

2
Solve by Completing the Square
x  6 x  16  0
2
x  6 x  16
2
+9
+9
x  6 x  9  25
2
 x  3  25
 x  3  5
x  3  5 x  8 x  2
2
Solve by Completing the Square
x  2x  5  0
2
x  2x  5
2
+1
+1
x  2x 1  6
2
 x  1  6
 x  1   6
2
x  1 6
Solve by Completing the Square
x  10 x  4  0
2
x  10 x  4
2
+25
+25
x  10 x  25  29
2
 x  5  29
2
x  5   29
x  5  29
Solve by Completing the Square
x  8 x  11  0
2
x  8 x  11
2
+16
+16
x  8 x  16  5
2
x  4  5
x  4   5
2
x  4  5
The sum or difference of two cubes will factor into a
binomial  trinomial.

a  b  a  b a  ab  b
3
3
2
2

same sign
always +
always opposite

a  b  a  b a  ab  b
3
3
2
2

same sign
always opposite
always +

a  b  a  b a  ab  b
3
3

2
2
a  b  a  b a  ab  b
3
3
2

2


 a  ba

 ab  b 
a  b  a  b a  ab  b
2
a b
2
3
3
3
3
2
2