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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cerverusdante cerverusdante · Answer 1 · 2020-03-17T02:52:26+01:00

Answer:

Sophie factor the trinomial completely.

Carlos didn't factor the trinomial completely.

Step-by-step explanation:

Let's factor the expression.

Notice that all the terms of [tex]-4x^{2} -10x+6[/tex] are divisible by -2, so let's factor -2 out:

[tex]-2(2x^{2} +5x-3)[/tex]

Now, we can factor [tex]2x^{2} +5x-3[/tex] step by step:

Step 1. Split the middle term

[tex]2x^{2} +6x-x-3[/tex]

Step 2. Group similar terms

[tex](2x^{2} -x)+(6x-3)[/tex]

Step 3. Factor each parentheses

[tex]x(2x-1)+3(2x-1)[/tex]

Step 4. Factor the common binomial out

[tex](2x-1)(x+3)[/tex]

Finally, we can put everything together:

[tex]-4x^2-10x+6=-2(2x-1)(x+3)[/tex] The same result as Sophie's!

We can conclude that Sophie factored the trinomial completely, whereas Carlos did not.