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

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 Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1: +3 & +1 +3 & +2 Factor completely 2 integers with: Product of: Sum of: +3 +4 +3 & +1 2 integers with: Product of: Sum of: +6 +5 +3 & +2 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1 - Continued +9 & -2 -8 & +2 -4 & -9 Factor completely 2 integers with: Product of: Sum of: -18 +7 +9 & -2 2 integers with: Product of: Sum of: -16 -6 -8 & +2 2 integers with: Product of: Sum of: +36 -13 -4 & -9 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 1 - Continued Always check for common factoring first!!! Factor completely Always check for common factoring first!!! 2 integers with: Product of: Sum of: +6 -5 -3 & -2 2 integers with: Product of: Sum of: +5 +3 Not such integers! Cannot further be factored, trinomial is not factorable. Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 2 – Factoring Special Trinomials Factor completely You can still think this way!! 2 integers with: Product of: Sum of: +7 & +7 +49 +14 You can still think this way!! 2 integers with: Product of: Sum of: +64 -8 & -8 -16 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 2 – Factoring Special Trinomials Factor completely Always check for common factoring first!!! You can still think this way!! 2 integers with: Product of: Sum of: +36 -12 -6 & -6 You can still think this way!! 2 integers with: Product of: Sum of: +25 +10 +5 & +5 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 3: More variables Factor completely 2 integers with: Product of: Sum of: 27 -12 -9 & -3 2 integers with: Product of: Sum of: -15 -2 -5 & +3 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Example 3: More variables - Continued Factor completely Always check for common factoring first!!! 2 integers with: Product of: Sum of: -6 +1 +3 & -2 2 integers with: Product of: Sum of: -3 +2 +3 & -1 Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

Homework Work sheet: Factoring Simple Trinomials Day 1: #1 – 5 Day 2: #6, 7 Text: Day 2: P. 307 #2, 3 Check the website for updates Factoring Simple Trinomials © 2017 E. Choi – MPM2D - All Rights Reserved

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