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.