Question

Determine whether x+2 is a factor of p(x)=x³+3x²+3x+1

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Answer 1

g(x) = x + 2 = 0

g(x) = x = -2

p(x) = x³ + 3x² + 3x + 1 = 0

By putting the value of x from g(x) in p(x), we get

p(-2) = (-2)³ + 3(-2)² + 3(-2) + 1

p(-2) = (-8) + 3(4) + (-6) + 1

p(-2) = -8 + 12 - 6 + 1

p(-2) = 4 - 5

p(-2) = -1

As we can see that the result of p(-2) is not equal to the result of p(x) or -1 ≠ 0.

Therefore,

x+2 is not a factor of x³ + 3x² + 3x + 1.