MCR 3U1
Date:_______________________
Unit 1: Functions and Algebraic Expressions
2.3 Factoring Polynomials
Notes:
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Factoring means to express a polynomial as a product of polynomials.
Factoring is the opposite of expanding, distributing or multiplying.
To factor a polynomial fully means that only 1 and -1 remain as common factors in
the factored expression.
To factor polynomials fully, you can use factoring strategies that include
o Dividing by the greatest common factor (GCF)
o Recognizing a factorable simple trinomial of the form ax2 + bx + c, where a = 1
o Recognizing a factorable complex trinomial of the form ax2 + bx + c, where a≠1
o Recognizing a polynomial that can be factored as a difference of squares:
 a2 – b2 = (a + b)(a – b)
o Recognizing a polynomial that can be factored as a perfect square:
 a2 + 2ab + b2 = (a + b)2 and a2 - 2ab + b2 = (a - b)2
o Factoring by grouping
Examples:
A. Common Factoring
1. Factor.
a) 3x + 12
b) 4x2y + 8xy2
B. Simple Trinomials: ax2 + bx + c, a = 1
2. Factor.
a) x2 + 8x + 12
b) x2 – 9x + 20
d) 3x2 + 3x – 18
Unit 1
c) 8x3 – 6x2y2 + 4x2y
c) x2 + 10x + 25
e) 8 + 7y – y2
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MCR 3U1
Date:_______________________
C. Complex Trinomials: ax2 + bx + c, a ≠ 1
3. Factor
a) 3x2 – 10x + 8
b) 6x2 + 13x – 5
c) 5x2 – 14x – 3
D. Difference of Squares
4. Factor.
a) x2 – 9
d) 9x2 – 16
E. Perfect Squares
5. Factor
a) x2 + 6x + 9
Unit 1
d) 10x2 – 22x + 4
b) x2 – 4
c) x2 + 81
e) 8x2 – 18y2
b) 9k2 – 24k + 16
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MCR 3U1
Date:_______________________
F. Factor by Grouping
6. Factor
a) 3x(y + 1) + 7z(y + 1)
b) ax + ay + 2x + 2y
c) ay2 + 3ay + 4y + 12
7. a) Write an algebraic expression for the area of the shaded region.
x+6
x–6
x+9
x+9
b) Write the area expression in factored form.
c) Substitute x = 7 into both forms. Are the results the same? Why?
Text Work: Page 102 # 1-7, 9, 11
Unit 1
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