1. Grade 10 Academic (MPM2D) Unit 3: Algebra & Quadratic Models Factoring Non-Simple Trinomials
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.
Factoring Non-Simple Trinomials
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3. Recall: 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
Factoring Non-Simple Trinomials
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4. Factoring a Non-Simple Trinomial
Common ways to factor a trinomial in the form
Decomposition method
Trial and Error (Guess & Check)
Decomposition formula
Others
Factoring Non-Simple Trinomials
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5. Decomposition Method +1 & +4 -1 & -2 Example 1:
Factor completely by decomposition method
2 integers with:
Product of ac:
Sum of b:
(+2)(+2)
 +4
 +5
+1 & +4
2 integers with:
Product of ac:
Sum of b:
(+2)(+1)
 +2
 -3
-1 & -2
Factoring Non-Simple Trinomials
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6. Decomposition Method -36 & -5 Example 1: Continued
Factor completely by decomposition method
2 integers with:
Product of ac:
Sum of b:
(+6)(+30)
 +180
 -41
-36 & -5
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

7. Trial and Error Method Example 2:
Factor completely by Trial and Error Method +3
Not match
Matched!!
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

8. Trial and Error Method Example 2: Continued
Factor completely by Trial and Error Method
Not match
Not match +8
Not match
Matched!
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

9. Trial and Error Method Example 2: Continued
Factor completely by Trial and Error Method
Not match
Not match +6
Not match
Not Match
Matched!!
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

10. Decomposition Formula
Example 3:
Factor completely by Decomposition Formula
2 integers with:
Product of ac:
Sum of b:
(+3)(-2)
 -6
 +1
+3 & -2
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

11. Decomposition Formula
Example 3: Continued
Factor completely by Decomposition Formula
2 integers with:
Product of ac:
Sum of b:
(+2)(+12)
 +24
 +11
+3 & +8
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

12. Decomposition Formula
Example 3: Continued
Factor completely by Decomposition Formula
2 integers with:
Product of ac:
Sum of b:
(+6)(-5)
 -30
 +13
+15 & -2
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

13. Homework
Work sheet: Factoring Non-Simple Trinomials Day 1: #1 – 8 Text: Check the website for updates
Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved

14. End of lesson Factoring Non-Simple Trinomials
© 2017 E. Choi – MPM2D - All Rights Reserved