The value of a polynomial $f (x) = 4 x^{3} + 3 x^{2} + 2 x + x$ at $x = 3$ is _____.

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Solution

The given polynomial is $f (x) = 4 x^{3} + 3 x^{2} + 2 x + x$ ,
then the value of $f (x)$ at a point $x = 3$ is
$f (3) = 4 (3)^{3} + 3 (3)^{2} + 2 (3) + 3$
$= 108 + 27 + 6 + 3$
$= 144$

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Statement1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .