Transcript lindsaythurber.rdpsd.ab.ca

Reviewing Concepts
• Lesson 29(3) will review the following
concepts:
• Dividing Exponent laws
• Dividing Polynomial by a Monomial
• Expanding Binomials ( FOIL)
• Factoring out the monomial (GCF)
• Factoring Trinomials
EXPONENT LAW 3
• QUOTIENT OF POWERS
• xa  xb = xa-b
Dividing Powers with the same base
6a5b3
3a2b2
Solution
6a5b3 means
3a2b2
6a5b3
3a2b2
=
6 a5 b3
x 2 x 2
3 a
b
6 a5 b3
x 2 x 2
3 a
b
= 2a3b
Dividing a Polynomial by a
Monomial
Divide 18mn – 4n + 2n2 by 2n.
18mn – 4n + 2n2
2n
18mn – 4n +
2n
2n 2n
2n2
9m – 2 + n
Remember your
Exponent Laws
for Division
Simply divide each
term by 2n
Expanding Binomials
Example: (x – 2)(x + 3)
F – Fist (x – 2)(x + 3)
O – Outside (x – 2)(x + 3)
I – Inside (x – 2)(x + 3)
L – Last (x – 2)(x + 3)
(x)(x) + (x)(3) + (-2)(x) + (-2)(3)
x2 + 3x – 2x – 6
x2 + x - 6
Factoring out the GCF
Factor: 4t + 12
Step 1 – Find the GCF
4t = 4 * t
12 = 4 * 3
GCF = 4
Step 2 – Divide to find the
other factor
4t + 12
= t+3
4
Therefore 4t + 12 = 4(t + 3)
Check by
expanding
4(t + 3)
4(t) +4(3) = 4t + 12
Factoring Trinomials
x2 + 7x + 6
What two
numbers add
up to +7
Factors:
Same two
numbers that
multiply to
give you +6
Therefore: x2 + 7x + 6
= (x + 1)(x + 6)
Sum:
1x6
1+6=7
-1 x -6
-1 + (-6) = - 7
2x3
2+3=5
-2 x -3
-2 + (-3) = - 5
Chart to Help with Signs
in Factoring Trinomials
Sum
(• 2nd Term)
Negative
Product
( 3rd Term)
Negative
Negative
Positive
Positive
Negative
Positive
Positive
INTEGERS
Bigger #(-)
Smaller # (+)
Both Negative
numbers
Bigger # (+)
Smaller # (-)
Both Numbers
Positive
SIMPLIFY
4x5y3
2x2y2
-8a6c3
2a2c
DIVIDE
30xy2
– 15x +
5y
10y2
6ab – 4a + 8b2
4a
EXPAND
(x – 5)(x + 6)
(x – 2)(x - 3)
(x + 5)(x + 7)
TAKE OUT THE COMMON
FACTOR
6t + 12
6t2
+ 12t - 18
-3x2 + 6x - 18
FACTOR COMPLETELY
x2 + 7x + 6
x2 - 8x - 16
x2 + 4x - 12
Class work
• Check solutions to lesson 29(2)
• Complete Lesson 29(3) worksheet.