Question

use the factor theorem whether g(x) is a factor of p(x) in this following case:
1:p(x)= x^3 + 3x^2 +3x + 1, g(x) = x+ z

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Answer 1

Apply remainder theorem

=>x + z =0

=> x = - z

Replace x by – z we get

=>x3 + 3x2 + 3x + 1

=>(-z)3 + 3(-z)2 + 3(-z) + 1

=> -z^3-3z^2-3z+1

=> -z^3-3z^2-3z+1 is your answer.