Download Lessons from D3 Skeleton Note MCF3MI U2

Unit 2 – Day 3 - Common Factoring
To factor an expression is to write it as a product.
It is the opposite of ________________________.
Common Factoring is the easiest type of factoring. It will always be the method of factoring that should be
attempted ___________.
Ex. 1 Find the GCF.
a) 24, 36, 60
b) 4x2, 10x3, 8x4
c) 2a(a - 3), 5(a - 3)
Ex. 2: Determine the greatest common factor. Use the GCF to factor the expression.
a) 3a - 9
b) x2 + 2x
c) 5a2 + 10a
e) 10x3 - 15x2
f) 3x2y + 12xy
g) 15a3b4c + 20a2b5c3
Ex. 3: Factors can sometimes be polynomials
i) a (2x+1)+b (2x+1)
ii) 2(a +b)-3c (a +b)
Ex. 4: Factor by grouping
i) bx + 3x + by + 3y
Ex. 5 Determine the unknown measurement.
Pg 93 # 2, 3, 5 – 9, 11, 15, 16
d) 2x3 + 6x2 - 12x
ii) 9m + 12 - 15m2 - 20m
iii) 4(r -t) -3s (t -r)
Warm up
Factor.
1) 5b - 10
3) 14x4 - 21x3
2) -8a + 12
4) 6a5b4 - 12a3b3 + 18a4b2
Unit 2 Day 4: Factoring Trinomials: x2 + bx + c
(x + 2)(x + 1) =
Steps for factoring trinomials of the form x2 + bx + c
1) Write two brackets with x at the front of each.
2) Fill in two numbers that
-
3) Check by expanding.
** Remember to pay attention to the signs!!
If numbers multiply to give a negative we know
If numbers multiply to a positive we know
Examples: Factor. (Remember to common factor first if possible!)
1) x2 - 4x + 3
4) a2 - 4a – 21
7) 3x2 - 12x
2) x2 + 14x + 40
5) n2 - n - 30
8) 2m2 + 10m – 48
3) x2 - 7x + 12
6) x2 + 2xy - 48y2
9) 4y2 - 8y – 60
10) c2 – 10c + 25
pg 99 # 2, 3, 5, 6, 7, 9, 14
Warm Up
Factor
a) x2 - x - 6
b) x2 + x – 6
c) 2x2 - 18x + 40
Unit 2 Day 5: Factoring Tricky Trinomials
Factor completely
4x2 - 8x - 12
common factor
sum & product
Not so tricky... but! Factor 2n2 + 7n + 6
Method 1: Factor using a chart.
2n2 + 7n + 6
Method 2: Factor using decomposition.
2n2 + 7n + 6
Examples: Factor
a) 3a2 - 17a + 20
b) 6p2 + 11p – 10
c) 16m2 – 26mn – 12n2
d) 5k2 – 17k - 4
Question:
5x - 4 is a factor of 5x2 + 26x - 24. What is the other factor?
How can you check to see if you have factored correctly?
p. 109 # 2, 4 – 6, 9, 10, 13, 14
Warm up
Factor
1) x2 - 6x + 9
2) 4x2 + 12x + 9
Unit 2 Day 6 – Special Quadratics
Perfect Square Trinomials
Factor
1) t2 -12t + 36
2) 25y2 + 40yz + 16z2
Pattern:
Difference of Squares
Factor
x2 - 25
Pattern:
Factor
1) 49y2 - 36
2) 36 - 9k2
3) 28x2 - 175y2
pg. 115 #2, 3, 4, 7, 11
4) a4 - 16
Unit 7 Review
1) Expand and simplify
 a) 2x(3x - 1) + 4(x2 + 3x + 3) - 2x(5x - 3)
 b) 2(x + 1)(3x - 7) - (x + 3)2
2) Factor fully.
 a) x2 + 2x - 35 
b) 9x – 36
c) 3x2 + 14x +8
d) x2 + xy + 2x + 2y
e) 2x3 - 6xy + 10x
f) 4x2 + 16x - 48
g) 2x2 – 50  
h) 9x2 - y2  
i) 6a3 - 4a2 - 16a
 j) 16x2 - 24x + 9  
k) (x+y)2 - 7(x+y) – 18
l) (x + 5)2 - (3x - 2)2
3) Determine the length of the rectangle, given the area and the width.
x-5
3x
A = 6x2 + 15x
A = x2 - 15x + 50
4) Determine two possible values of k to make each expression factorable.
a) x2 + kx + 12
b) x2 - 2x + k