Two students, Carlos and Sophie, factored the trinomial -4x2 − 10x + 6. Sophie factored it as -2(2x − 1)(x + 3) and Carlos facto

Question

2 years ago

6

Two students, Carlos and Sophie, factored the trinomial -4x2 − 10x + 6. Sophie factored it as -2(2x − 1)(x + 3) and Carlos facto

red it as (x + 3)( -4x + 2). Indicate which student factored the trinomial completely and which student did not, and explain why. (10 points)

Mathematics

1 answer:

damaskus [11] · Answer 1 · 2022-07-28T20:07:48+03:00

Sophie has factored the term completely while Carlos has not factored the term completely.

Step-by-step explanation:

We need to factor the trinomial:

$-4x^2-10x + 6$

Factoring:

$-4x^2-10x + 6\\Taking\,\,-2\,\,common:\\-2(2x^2+5x-3)\\Now\,\,factoring:\\-2(2x^2+6x-x-3)\\-2(2x(x+3)-1(x+3))\\-2(2x-1)(x+3)$

So, the factored form of $-4x^2-10x + 6$ is $-2(2x-1)(x+3)$

So, Sophie has factored the term completely. The terms are factored when we cannot further simplify it. Since Carlos factored (x+3)(-4x+2) 2 can be taken common from the term (-4x+2) so, it is not factored completely.

Keywords: Factoring the terms

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