The Laplace transform of the function— f(t) = t3 + 3t2

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The Laplace transform of the function—
f(t) = t³ + 3t² – 6t + 4

1. 6 + 2 – 6 + 4
  s⁴ s³ s² s
2. 6 + 6 – 6 + 4
  s⁴ s³ s² s
3. 6 – 6 + 6 – 4
  s⁴ s³ s² s
4. 6 – 6 + 6 + 4
  s⁴ s³ s² s

Correct Option: B

L{f(t)} = L{t³ + 3t² – 6t + 4}

=	3!	+	3·2!	–	6·1!	+	4
	s⁴		s³		s²		s

=	3·2·1	+	3·2·1	–	6·1	+	4
	s⁴		s³		s²		s

=	6	+	6	–	6	+	4
	s⁴		s³		s²		s

Hence, alternative (B) is the correct answer.