Part CCSIR NET June 2025differencing-and-differentiating-both-drop-the-degree-so-three-vectors-land-in-a-plane

Differencing and differentiating both drop the degree so three vectors land in a plane

Let V be the $R -$ vector space of all polynomials with real coefficients. Let $f (x) = x^{2} + x + 1$ . Which of the following subsets of V are linearly independent?

A.{f′(x), f(x) − f(x − 1), 1}
B.{f(x + 1) − f(x), f(x) − f(x − 1), 1}
C.{f(x), f′(x), 1}✓
D.{f(x + 1), f(x − 1), f(x)}✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Differencing and differentiating both drop the degree so three vectors land in a plane

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