1. Grade 11 University: (MCR3U) Unit 1: Algebra & Quadratic Functions Review of Factoring 2
Mr. Choi
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2. Factoring a Polynomials
A polynomial is factored when it is written as the product of polynomials. We will consider that a polynomial is completely factored when no more variable factors can be removed and no more integer factors, other than 1 or -1, can be removed.
Review of Factoring 2
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3. Example 1 – Factoring Special Trinomials
Factor completely
You can still think this way!!
2 integers with:
Product of:
Sum of:
-8 & -8
+64
-16
Will be reviewed more later!!
You can still think this way!!
2 integers with:
Product of:
Sum of:
+25
+5 & +5
+10
Review of Factoring 2
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4. Factoring a Trinomial To factor a trinomial in the form
Remove any common factors
Write x as the first term in each binomial factor
Write the second terms, which are two numbers whose sum is b and whose product is c
Review of Factoring 2
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5. Example 2: Factoring Trinomials x2+bx+c
Factor completely
2 integers with:
Product of:
Sum of:
+12 -7
-4 & -3
2 integers with:
Product of:
Sum of: -9 -8
-9 & +1
Review of Factoring 2
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6. Example 2: Continued +2 & +5 -4 & +2 Factor completely
2 integers with:
Product of:
Sum of: 10 7
+2 & +5
2 integers with:
Product of:
Sum of: -8 -2
-4 & +2
Review of Factoring 2
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7. Factoring a Non-Simple Trinomial
Common ways to factor a trinomial in the form
Decomposition method
Trial and Error (Guess & Check)
Decomposition formula
CHOI’s Method
Review of Factoring 2
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8. Example 2: Factoring Trinomials ax2+bx+c
Factor completely:
By Decomposition method
2 integers with:
Product of ac:
Sum of b:
(+2)(+6)
 +12
 +7
+3 & +4
By Trials & Errors method +6
Not match
Matched!!
Review of Factoring 2
© 2017 E. Choi – MCR3U - All Rights Reserved

9. Example 2: Factoring Trinomials ax2+bx+c
Factor completely:
Recall
2 integers with:
Product of ac:
Sum of b:
(+2)(+6)
 +12
 +7
+3 & +4
By: CHOI’s Method:
Box Method
Reduce!!
Review of Factoring 2
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10. Example 2: Factoring Trinomials - Continued
Factor completely:
By Decomposition method
2 integers with:
Product of ac:
Sum of b:
(+6)(-2)
 -12
 -1
-4 & +3
By Decomposition formula
2 integers with:
Product of ac:
Sum of b:
(+6)(-2)
 -12
 -1
-4 & +3
Review of Factoring 2
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11. Example 2: Factoring Trinomials - Continued
By Trials and Errors Method
Not match
Not match -2
Not match
Not Match
Matched!!
Factoring Non-Simple Trinomials
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12. Example 2: Factoring Trinomials - Continued
Factor completely:
Recall:
2 integers with:
Product of ac:
Sum of b:
(+6)(-2)
 -12
 -1
-4 & +3
By CHOI’s Method
Box Method
Reduce!!
Review of Factoring 2
© 2017 E. Choi – MCR3U - All Rights Reserved

13. Example 2: Factoring Trinomials - Continued
Factor completely:
By Decomposition method
2 integers with:
Product of ac:
Sum of b:
(+14)(+3)
 +42
 -13
-6 & -7
By Decomposition formula
2 integers with:
Product of ac:
Sum of b:
(+14)(+3)
+42
 -13
-6 & -7
Review of Factoring 2
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14. Example 2: Factoring Trinomials - Continued
By Trials and Errors Method
Not match
Not match +3
Not match
Matched!!
Review of Factoring 2
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15. Example 2: Factoring Trinomials - Continued
Recall
2 integers with:
Product of ac:
Sum of b:
(+14)(+3)
 42
 -13
-7 & -6
By CHOI’s Method
Box Method
Reduce!!
Review of Factoring 2
© 2017 E. Choi – MPM3R - All Rights Reserved

16. Example 4: Combining Factoring Techniques
Factor completely:
2 integers with:
Product of ac:
Sum of b:
(+6)(-5)
 -30
 +13
+15 & -2
By CHOI’s Method
Reduce!!
Review of Factoring 2
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17. Example 4: Combining Factoring Techniques
Factor completely:
Review of Factoring 2
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18. Example 4: Combining Factoring Techniques
Factor completely:
Review of Factoring 2
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19. Homework
Work sheet: Review of Factoring 2 Text: Check the website for updates
Review of Factoring 2
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20. End of lesson Review of Factoring 2
© 2017 E. Choi – MCR3U - All Rights Reserved