Simplify (x^3-6)/(x-1) using long division. Select all correct ways of expressing this quotient. x^2+x+1+(-5)/(x-1) x^2+x+1+(5)/(x-1) x^2+x+1+(5)/(1-x) D x^2+x+1-(5)/(x-1) x^2+x+1-(5)/(1-x)

To simplify using long division, we divide by .Step 1: Divide the first term of the numerator by the first term of the denominator: .Step 2: Multiply the entire denominator by the result from Step 1: .Step 3: Subtract the result from Step 2 from the numerator: .Step 4: Divide the first term of the new numerator by the first term of the denominator: .Step 5: Multiply the entire denominator by the result from Step 4: .Step 6: Subtract the result from Step 5 from the new numerator: .Step 7: Divide the first term of the new numerator by the first term of the denominator: .Step 8: Multiply the entire denominator by the result from Step 7: .Step 9: Subtract the result from Step 8 from the new numerator: .Step 10: Write the final answer as the quotient plus the remainder divided by the denominator: .Therefore, the correct ways of expressing this quotient are:- -