i still don't get how do you divide

(3q cubed +q+6)/(q-2)
help!=]
i also need help in...
the volume of a rectangular prism is
2x cubed + x -2. the height of the prism is 2x-1, and the length of the prism is x+2. find the width of the prism.

im confused

To answer your first question, you need to review polynomial long division. You will be left with a remainder.

I got the answer to be
3q^2 +6q +12 + [30/(q-2)]
The term in brackets is the remainder

For your second question, the answer will be the volume divided by the area of the side that you know, or
(2x^3 +x -2)/(2x^2 +3x -3)
This also results in a remainder term. The denominator is not a monomial factor of the numerator.

The assigned you a pair of rather messy problems.

For a review/tutorial of what polynomial long division is all about, see

http://www.purplemath.com/modules/polydiv2.htm

To divide the expression (3q^3 + q + 6)/(q - 2), you can use polynomial long division. Here are the steps to follow:

Step 1: Ensure that the numerator and denominator are arranged in descending powers of the variable. If necessary, rewrite the expression in the correct order: (3q^3 + 0q^2 + q + 6)/(q - 2).

Step 2: Divide the first term of the numerator (3q^3) by the first term of the denominator (q) to get the first term of the quotient. In this case, 3q^3 divided by q gives us 3q^2.

Step 3: Multiply the entire denominator (q - 2) by the first term of the quotient (3q^2) and write the result below the numerator.

(3q - 6q^2)
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q - 2 | 3q^3 + 0q^2 + q + 6

Step 4: Subtract the result obtained in step 3 from the numerator. In this case, subtract (3q - 6q^2) from (3q^3 + 0q^2 + q + 6) to get (-6q^2 + q + 6).

Step 5: Bring down the next term from the numerator, which is q in this case.

(3q - 6q^2)
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q - 2 | 3q^3 + 0q^2 + q + 6
-(-6q^2 + q + 6)
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7q^2 + 0q - 2

Step 6: Repeat steps 2-5 using the new expression (7q^2 + 0q - 2) as the numerator.

Step 7: Divide the first term of the new numerator (7q^2) by the first term of the denominator (q) to get the next term of the quotient. In this case, 7q^2 divided by q gives us 7q.

Step 8: Multiply the entire denominator (q - 2) by the new term of the quotient (7q) and write the result below the new numerator.

(3q - 6q^2 + 7q - 14)
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q - 2 | 3q^3 + 0q^2 + q + 6
-(-6q^2 + q + 6)
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(7q^2 + 0q - 2)
- (7q^2 - 14q)
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14q + 6
Step 9: Repeat steps 2-5 using the new expression (14q + 6) as the numerator.

Step 10: Divide the first term of the new numerator (14q) by the first term of the denominator (q) to get the last term of the quotient. In this case, 14q divided by q gives us 14.

Step 11: Multiply the entire denominator (q - 2) by the last term of the quotient (14) and write the result below the new numerator.

(3q - 6q^2 + 7q - 14 + 14)
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q - 2 | 3q^3 + 0q^2 + q + 6
-(-6q^2 + q + 6)
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(7q^2 + 0q - 2)
- (7q^2 - 14q)
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(14q + 6)
- (14q - 28)
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34

Step 12: Since we have reached a constant term (34) with no remaining terms in the numerator, we have completed the division.

Therefore, the result of dividing (3q^3 + q + 6) by (q - 2) is 3q^2 + 7q + 14 with a remainder of 34.

For the second question, we are given the volume of a rectangular prism, which is 2x^3 + x - 2. The height of the prism is 2x - 1, and the length is x + 2. We need to find the width.

The volume formula for a rectangular prism is:
Volume = length * width * height

In this case, we know the volume is 2x^3 + x - 2, the height is 2x - 1, and the length is x + 2.

Plugging in these values into the volume formula, we get:
2x^3 + x - 2 = (x + 2) * width * (2x - 1)

To find the width, we can isolate it by dividing both sides of the equation by (x + 2) * (2x - 1):

(2x^3 + x - 2) / [(x + 2) * (2x - 1)] = width

Therefore, the width of the prism is equal to (2x^3 + x - 2) divided by [(x + 2) * (2x - 1)].