If (x+1) divides \( \Large x^{3}-px^{2}-4x+1 \) and the remainder is zero, then the value of p is
Correct Answer: Description for Correct answer:
\( \Large \left(x+1\right) is\ a\ factor\ of\ 3x^{3}-px^{2}-4x+1 \)
\( \Large \left(f-1\right) = 0, \)
\( \Large f \left(x\right)=3x^{3}-px^{2}-4x+1=0,\ if\ f \left(-1\right)=0 \)
\( \Large f \left(-1\right) = \left(3 \left(-1\right)^{3}-p \left(-1\right)^{2}-4 \left(-1\right)+1 \right) = 0 \)
\( \Large -3-p+4+1 = 0 \)
\( \Large -p+2 = 0, => p = 2 \)
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