Question

X³ + 3x² + 3x + 1 / x+1

Answer 1

$p(x) = {x}^{3} + 3 {x}^{2} + 3x + 1$

By remainder theorem

x + 1 = 0

x = -1

Putting value of x in p(x)

$p( - 1) = { - 1}^{ 3} + 3 { - 1}^{2} + 3( - 1) + 1$

$p( - 1) = - 1 + 3(1) - 3 + 1$

$p( - 1) = 0$

Hence x+1 is a factor of p(x)

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