Grade 10 Academic (MPM2D) Unit 3: Algebra & Quadratic Models Factoring Non-Simple Trinomials Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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 © 2017 E. Choi – MPM2D - All Rights Reserved

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

Trial and Error Method Example 2: Factor completely by Trial and Error Method +3 + 1 + 3 + 3 + 1 Not match Matched!! Factoring Non-Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Trial and Error Method Example 2: Continued Factor completely by Trial and Error Method - 1 - 8 - 8 - 1 Not match Not match +8 - 2 - 4 - 4 - 2 Not match Matched! Factoring Non-Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Trial and Error Method Example 2: Continued Factor completely by Trial and Error Method - 2 - 3 - 3 - 2 Not match Not match +6 - 1 - 6 - 1 - 6 - 2 - 3 Not match Not Match Matched!! Factoring Non-Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

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

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 + 3 +8 Factoring Non-Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

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 +15 - 2 Factoring Non-Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

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

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