Given that (x−1) is a factor of x^3+3x^2+x−5, factorize this cubic fully.

Medenovgj 2022-09-26 Answered
Given that ( x 1 ) is a factor of x 3 + 3 x 2 + x 5, factorize this cubic fully.
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Answers (1)

nutnhonyl8
Answered 2022-09-27 Author has 8 answers
The discriminant of your polynomial is Δ = 4 2 4 5 < 0
so this has no real roots, that is, factorization over R is finished. On the other hand, factorization over C is possible, yielding
x 2 + 4 x + 5 = ( x + 2 ) 2 + 1 = ( x + 2 i ) ( x + 2 + i )
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