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Find the remainder when $x^3+ 3x^2 + 3x + 1$ is divided by $ x $
Given:
$x^3+ 3x^2 + 3x + 1$ is divided by $x$
To do:
We have to find the remainder when $x^3+ 3x^2 + 3x + 1$ is divided by $x$.
Solution:
The remainder theorem states that when a polynomial, $p(x)$ is divided by a linear polynomial, $x - a$ the remainder of that division will be equivalent to $p(a)$.
Let $f(x) = x^3+ 3x^2 + 3x + 1$ and $g(x) = x-0$
So, the remainder will be $f(0)$.
$f(0) = (0)^3+3(0)^2+3(0) + 1$
$= 0+0+0+1$
$=1$
Therefore, the remainder is $1$.
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