Simplify using long division.Show all work.

(-72-4x^2+8x^3-36x)/(x-3)

Also,please solve (8b^3-6)/(2b-1)

I greatly appreciate your help.

try here. It shows all the steps.

http://calc101.com/webMathematica/long-divide.jsp

To simplify the expression (-72-4x^2+8x^3-36x)/(x-3) using long division, follow these steps:

Step 1: Arrange the terms in descending powers of x.

The expression becomes: 8x^3 - 4x^2 - 36x - 72.

Step 2: Divide the first term, 8x^3, by the leading term of the divisor, x.

The result is 8x^2.

Step 3: Multiply the result from Step 2 by the entire divisor, x-3.

(8x^2) * (x-3) = 8x^3 - 24x^2.

Step 4: Subtract the term obtained in Step 3 from the original expression.

(8x^3 - 4x^2 - 36x - 72) - (8x^3 - 24x^2) = -4x^2 - 36x - 72 + 24x^2.

Step 5: Bring down the next term.

The result is 20x^2 - 36x - 72.

Step 6: Repeat Steps 2 to 5 until there are no more terms.

Divide 20x^2 by x gives 20x.
Multiply (20x) * (x-3) to get 20x^2 - 60x.
Subtract (20x^2 - 36x - 72) - (20x^2 - 60x) = 24x - 72.
Divide 24x by x gives 24.
Multiply (24) * (x-3) to get 24x - 72.
Subtract (24x - 72) - (24x - 72) = 0.

Therefore, the simplified form is 8x^2 + 20x + 24.

Moving on to the next expression, (8b^3-6)/(2b-1):

Step 1: Divide the first term, 8b^3, by the leading term of the divisor, 2b.

The result is 4b^2.

Step 2: Multiply the result from Step 1 by the entire divisor, 2b - 1.

(4b^2) * (2b - 1) = 8b^3 - 4b^2.

Step 3: Subtract the term obtained in Step 2 from the original expression.

(8b^3 - 6) - (8b^3 - 4b^2) = -6 + 4b^2.

Therefore, the simplified form is 4b^2 - 6.

I hope this helps! If you have any further questions, feel free to ask.