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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Updated on: 10-Oct-2022

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