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.

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 are divisible by -2, so let's factor -2 out:

Now, we can factor step by step:

Step 1. Split the middle term

Step 2. Group similar terms

Step 3. Factor each parentheses

Step 4. Factor the common binomial out

Finally, we can put everything together:

The same result as Sophie's!

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

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: