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, as she factored out a term that Max left in his factorization.

Answer 2

Answer

Ann factored it correctly

Max did not factor it completely

The correct factorization is as shown.

Explanation

4x² − 6x − 4

The product of this equation = 4 × -4

                                                = -16

Sum = -6

Find 2 numbers that you can multiply to get -16 and when you add the same numbers you get -6.

The numbers are: -8 and 2

4x² − 6x − 4 = 4x² -8x + 2x − 4

                     = (4x² - 8x) + (2x − 4)

                     = 4x(x - 2) + 2(x - 2)          

                    =  (x - 2)(4x + 2)

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