Algebra 2, Trigonometry Name: Lesson 2.3 – Factoring Trinomials (a=1) Aim: I can factor trinomials where a=1 using diamond game Chill Stuff 1. Determine the two numbers that satisfy the given product AND sum below. (a) Product: 18, sum: 9 b) Product: 48, sum: -19 c) Product: -24, sum: -5 (d) Product: -36, sum: 5 Important Stuff 2. Factor the following trinomials (a) 𝑥! + 2𝑥 − 35 (b) 𝑥! + 11𝑥 + 24 (c) 𝑥! − 13𝑥 + 22 (d) 𝑥! − 5𝑥 − 50 (a) 𝑥! − 5𝑥 + 6 (b) 𝑥! − 15𝑥 + 44 (c) 𝑥! + 21𝑥 + 20 (d) 𝑥! − 6𝑥 − 16 3. Factor the following trinomials completely! (a) 5𝑏! + 15𝑏 − 50 (b) 2𝑥! − 4𝑥! − 30𝑥 (c) −2𝑘! − 4𝑥 + 16 (d) 4𝑝! + 36𝑝! + 32𝑝

Neat Stuff 4. Two students have attempted to factor 𝑥! + 6𝑥 − 16. Is either of them correct? Explain your reasoning. Student A Student B 𝑥! + 6𝑥 − 16 = (𝑥 + 2)(𝑥 − 8) 𝑥! + 6𝑥 − 16 = (𝑥 − 2)(𝑥 + 8)

5. Complete the table below.

6. Complete the table

7. Ms. G and Mr. Whittaker, the other Algebra 2/Trig teacher, tried to factor the following trinomial:

2𝑥! − 4𝑥 − 6. Ms. G got (2𝑥 − 6)(𝑥 + 1) and Mr. Whittaker got (2𝑥 + 2)(𝑥 − 3) (a) Verify that both of their products are correct factorizations of 2𝑥! − 4𝑥 − 6 by double distributing or FOILing (b) Why are neither of these completely factored? Explain.

Trinomial 𝑥! + 𝑏𝑥 + 16 𝑥! + 𝑏𝑥 + 10 𝑥! + 𝑏𝑥 − 36 𝑥! + 𝑏𝑥 − 24

List the possible “b” values that make the trinomial factorable

Trinomial 𝑥! + 𝑏𝑥 + 14 𝑥! + 𝑏𝑥 + 12 𝑥! + 𝑏𝑥 − 50 𝑥! + 𝑏𝑥 − 32

Determine the Missing Factor

(𝑥 − 7)(_______)

(𝑥 + 6)(_______)

(𝑥 + 5)(_______)

(𝑥 − 4)(_______)

Determine the “b” value