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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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Sophie factored it completely while Carlos did not.

Complete factoring is achieved when all factors other than monomial factors are prime factors. Carlos' (4x + 2) can still be factored into 2(x+1).

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