Using factor theorem, factorize each of the following polynomials:

x³ + 6x² + 11x + 6

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Solution

Let f(x) = x³ + 6x² + 11x + 6 be the given polynomial.

Now, put the we get

Therefore, is a factor of f(x).

Now,
$f (x) = x^{3} + 5 x^{2} + x^{2} + 5 x + 6 x + 6$

Hence, are the factors of f(x).

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