Question

wo students, Ann and Max, factored the trinomial 4x2 − 6x − 4. Ann factored it as 2(x − 2)(2x + 1) and Max factored it as (x − 2)(4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.

Answer 1

Factored completely means ALL common factors have been taken out. Ann factored it correctly 2(x-2)(2x+1)

Answer 2

Answer: Ann. Max answer is not complete because he could use the common factor for the (4x + 2) = 2(2x + 1)

Step-by-step explanation: 4x² - 6x - 4

Common factor: 4x² - 6x - 4 = 2(2x² - 3x - 2) =

product of 2 binomials: 2x² - 3x - 2 = 0

a = 2 b=-3 c=-2

Δ = (-3)² - 4.2.(-2) = 9 + 16 = 25

√Δ = 5

x = 3±5/4

x₁ = 3+5/4 = 8/4 = 2

x₂ = 3-5/4 = -2/4 = -1/2

a(x-x₁)(x-x₂) = 2 (x+1/2)(x-2)=(2x + 1)(x - 2)

So 2(2x² - 3x - 2) = 2(2x + 1)(x - 2)

Max answer is (x − 2)(4x + 2) is not complete because he could use the common factor for the (4x + 2) = 2(2x + 1)