Question

Two students, Carlos and Sophie, factored the trinomial -4x² − 10x + 6. Sophie factored it as -2(2x − 1)(x + 3) and Carlos factored it as (x + 3)( -4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why.

Answer 1

Sophie factored completely.

Carlos did not factor out a 2 out of his last term

Explanation:

-4x² − 10x + 6

Sophie factored it as -2(2x − 1)(x + 3) and Carlos factored it as (x + 3)( -4x + 2).

If you look at the last term in Carlos

(x + 3)( -4x + 2)

You can factor out a -2

(x+3) (-2)(2x-1)

It is not factored completely with the negative two inside the parentheses

He could also have factored out a 2

(x+3) (2)(-2x+1)

I like having a positive x so I use the -2

Either would be acceptable.