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.

Question

Mathematics

Laylah

9 August, 18:46

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.

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Answers (1)

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Livia · Answer 1

Sophie factored completely.

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

Step-by-step 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.