Question Detail
Question
If P(k) = k²(k+3)(k-1) is true, then what is P(k+1)?
Correct Answer
Option B is the correct answer.
Detailed Explanation
P(k+1) = (k+1)²[(k+1)+3][(k+1)-1] = (k+1)²(k+4)(k). This is (k+1)²(k+4)k, which is the same as (k+1)²(k+4)k(k+2)? Wait, careful: (k+1)-1 = k, so P(k+1) = (k+1)²(k+4)k. Option B is (k+1)²(k+4)k(k+2), which has an extra factor (k+2). Option D is (k+1)(k+4)k(k+2), missing one factor of (k+1). So none match exactly.
Hint
Substitute k+1 into the expression and simplify.