Divide. (2x^3 – x^2 – 24x + 12) ÷ (2x – 1)
A. x^2 – 1
B. x^2 – 12
C. 2x – 1
AAAaannndd the bot gets it wrong yet again!
Clearly, dividing a cubic by a linear factor will yield a quadratic quotient.
B. x^2 - 12
since 2x^3 – x^2 – 24x + 12 = (2x-1)(x^2-12)
I apologize for the mistake in my previous response. You are correct, the quotient is indeed a quadratic. The correct answer is B. x^2 - 12. Thank you for bringing this to my attention.
To divide (2x^3 – x^2 – 24x + 12) by (2x – 1), we can use polynomial long division. Here are the steps:
Step 1: Write the dividend (2x^3 – x^2 – 24x + 12) in descending powers of x. Rewrite any missing terms with a coefficient of 0.
2x^3 – x^2 – 24x + 12
Step 2: Divide the first term of the dividend (2x^3) by the first term of the divisor (2x). This gives the first term of the quotient.
(2x^3) ÷ (2x) = x^2
Step 3: Multiply the divisor (2x – 1) by the first term of the quotient (x^2), and write the result below the dividend.
(2x – 1) * (x^2) = 2x^3 – x^2
Step 4: Subtract the result obtained in step 3 from the dividend.
(2x^3 – x^2 – 24x + 12) - (2x^3 – x^2) = -24x + 12
Step 5: Bring down the next term from the dividend (–24x).
-24x + 12
Step 6: Repeat steps 2 to 5 with the new dividend (-24x + 12).
(-24x) ÷ (2x) = -12
(2x – 1) * (-12) = -24x + 12
(-24x + 12) - (-24x + 12) = 0
Step 7: Since the new dividend is now 0, we stop the division. The quotient obtained so far is x^2 – 12, and the remainder is 0.
Therefore, the correct answer is B. x^2 – 12.