Divide
28
𝑥
2
−
7
𝑥
21
𝑥

Question

Divide 
28
𝑥
2
−
7
𝑥
21
𝑥

BlackTom AI · Accepted Answer

The task presents a division problem: divide 28x^2 − 7x by 21x. 
Option 1: 7x. This would come if you cancelled in a way that leaves 7x, but the original expression has a higher degree and a factor of 4x−1 hidden in the numerator, so 7x is not the correct simplification. 
Option 2: (4x − 1)/3. This matches the standard simplification: factor the numerator 28x^2 − 7x = 7x(4x − 1). Then divide by the denominator 21x to get [7x(4x − 1)]/(21x) = (4x − 1)/3 after cancelling the common factors 7 and x with 21x. This is the correctly reduced form. 
Option 3: 12x − 3. This would imply a different factorization or cancellation pattern, but it does not arise from simplifying [28x^2 − 7x]/(21x); the coefficients do not align with the actual cancellation, so this is incorrect. 
Option 4: 4x − 1. This is what you would get if you forgot to divide by 3, i.e., if you cancelled only part of the denominator or omitted the remaining factor of 1/3. It is missing the essential division by 3, so it does not equal the original expression after full simplification. 
In summary, Option 2 precisely captures the proper simplified form after factoring the numerator and canceling common factors with the denominator, while Options 1, 3, and 4 misrepresent the result by either omitting necessary divisions or misapplying cancellations.

Divide 28 𝑥 2 − 7 𝑥 21 𝑥

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