Divide. (2x^3 - x^2 - 24x + 12) divided by (2x - 1)
To divide (2x^3 - x^2 - 24x + 12) by (2x - 1), we can use polynomial long division.
Here's the division process step by step:
Step 1: Divide the leading term of the dividend by the leading term of the divisor:
2x^3 / 2x = x^2
Step 2: Multiply the divisor by the result obtained in step 1, and subtract this from the dividend:
(2x - 1) * x^2 = 2x^3 - x^2
(2x^3 - x^2 - 24x + 12) - (2x^3 - x^2) = -23x + 12
Step 3: Repeat steps 1 and 2 with the result obtained in step 2:
(-23x) / (2x) = -11.5
(2x - 1) * (-11.5) = -23x + 11.5
(-23x + 12) - (-23x + 11.5) = 0.5
Step 4: Since the result of step 3 is a constant term, divide it by the leading term of the divisor to get the remainder:
0.5 / 2x = 0.25
Therefore, the result of dividing (2x^3 - x^2 - 24x + 12) by (2x - 1) is x^2 - 11.5 + 0.25, and the remainder is 0.25.