Simplify: $3 n^{3} + 22 n^{2} + 45 n + 26$

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Solution

$f (n) = 3 n^{3} + 22 n^{2} + 45 n + 26$
we need to simplify it
$∴ f (n) = 0$
$3 n^{3} + 22 n^{2} + 45 n + 26 = 0$
by substituting random n find a value of n for which $f (n) = 0$
$n = 1$
$∴ (n + 1)$ is a factor of $f (n)$
$f (n) = (n + 1) (3 n^{2} + 19 n + 26)$
$= (n + 1) (3 n^{2} + 6 n + 13 n + 26) = (n + 1) (3 n (n + 2) + 13 (n + 2))$
$= (n + 1) (n + 2) (3 n + 13)$

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