Question

Two 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

Ann factored it completely because she took the 2 out.

Max's second factor 4x - 2 can be factored further to 2 (2x - 1)

Answer 2

Ann factored the trinomial completely

take out a common factor of 2

2(2x² - 3x - 2 )

to factor the trinomial consider the factors of the product 2 × - 2 = - 4 which sum to - 3

These are - 4 and + 1

Split the middle term using these factors

2x² - 4x + x - 2 ← ( factor by grouping )

= 2x(x - 2) + 1(x - 2) ← ( take out common factor (x - 2) )

=(x - 2)(2x + 1)

4x² - 6x - 4 = 2(x - 2)(2x + 1) ← ( fully factored )