please check my answers and help me with the last one please, I cant get it to come out right.

Divide using long division or synthetic division.

2.(x^2 + 13x + 40)/ (x + 5)
I got x + 8

5. 3m^3+7m^2-16m+16/ m+4
i got 3m^2-5m+4

7.(21x^3 - 7)/(3x - 1)(this one I cant get the anwswer to match up with my answer choices.)

all right, on 7), the answer is obvious, as the numerator (with 7 factored out) is a difference of two cubes, one factor dividing out the denominator. So you can't do that, I know, but I don't know how I can help you as I can't do division here. I did it on paper, and I get the right answer.

Let's go through each problem to verify your answers:

2. (x^2 + 13x + 40) / (x + 5):
To divide using long division, we start by dividing the first term of the numerator (x^2) by the first term of the denominator (x). This gives us x. Then, we multiply x by the entire denominator (x + 5) to get x(x + 5) = x^2 + 5x. Subtracting this from the numerator, we get (x^2 + 13x + 40) - (x^2 + 5x) = 8x + 40. Now, we repeat the process by dividing 8x by x, which gives us 8. Multiplying 8 by the denominator, we have 8(x + 5) = 8x + 40. Subtracting this from the remaining terms, we get (8x + 40) - (8x + 40) = 0. Since there are no remaining terms, our final quotient is x + 8, which matches your answer. Therefore, your answer is correct.

5. (3m^3 + 7m^2 - 16m + 16) / (m + 4):
Again, using long division, we start by dividing the first term of the numerator (3m^3) by the first term of the denominator (m). This gives us 3m^2. Then, we multiply 3m^2 by the entire denominator (m + 4) to get 3m^2(m + 4) = 3m^3 + 12m^2. Subtracting this from the numerator, we get (3m^3 + 7m^2 - 16m + 16) - (3m^3 + 12m^2) = -5m^2 - 16m + 16. Now, we repeat the process by dividing -5m^2 by m, which gives us -5m. Multiplying -5m by the denominator, we have -5m(m + 4) = -5m^2 - 20m. Subtracting this from the remaining terms, we get (-5m^2 - 16m + 16) - (-5m^2 - 20m) = 4m + 16. Since there are no remaining terms, our final quotient is 3m^2 - 5m + 4, which matches your answer. Therefore, your answer is correct.

Now, let's move on to the last problem:

7. (21x^3 - 7) / (3x - 1):
To divide this using long division, we start by dividing the first term of the numerator (21x^3) by the first term of the denominator (3x). This gives us 7x^2. Then, we multiply 7x^2 by the entire denominator (3x - 1) to get 7x^2(3x - 1) = 21x^3 - 7x^2. Subtracting this from the numerator, we get (21x^3 - 7) - (21x^3 - 7x^2) = -7x^2 - 7.

At this point, we can't proceed further because the degree of the remaining terms (-7x^2 - 7) is less than the degree of the denominator (3x - 1). Consequently, the division is not possible using long division.

To confirm this, let's use synthetic division as an alternative approach:
In synthetic division, we set up the division as follows:

1/3 | 21 0 -7
-----------------

Now, we bring down the first coefficient, which is 21:

1/3 | 21 0 -7
-----------------
21

Next, we perform the synthetic division by multiplying the result (21) by the divisor (1/3) and adding it to the next coefficient (0):

1/3 | 21 0 -7
-----------------
21
------------
0

Then, we bring down the next coefficient, which is 0:

1/3 | 21 0 -7
-----------------
21
------------
0 0

Finally, we bring down the last coefficient, which is -7:

1/3 | 21 0 -7
-----------------
21
------------
0 0
------------
-7

Based on the synthetic division, we have a remainder of -7.

Therefore, the correct answer for problem 7 is (21x^3 - 7) / (3x - 1) with a remainder of -7.