Question

find the remainder when x³-2x²+x+1 is divided by x-1

Answer 1

this is the ans
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Answer 2

Answer:

The remainder will be 1.

Step-by-step explanation:

Given: $x^3-2x^2+x+1$

We have to find the remainder when $x^3-2x^2+x+1$is divided by x-1.

We are solving in the following way:

We have,

$x^3-2x^2+x+1$

For finding the remainder, we need to use the remainder theorem.

Let assume,

$p(x)=x^{3}-2 x^{2}+x+1$

Hence, to find the remainder on dividing by x−1, we need to equate it to 0 and put that value of x in p(x).

Then,

$\begin{array}{l}\Rightarrow x-1=0 \\\Rightarrow x=1\end{array}$

Hence, we get the value of x is 1.

Now, we will put this value of x in$p(x)=x^{3}-2 x^{2}+x+1$.

$\begin{array}{l}\mathrm{p}(1)=1^{3}-2 \times 1^{2}+1+1\\\mathrm{p}(1)=1-2\times1+1+1\\\mathrm{p}(1)=1-2+1+1 \\\mathrm{p}(1)=1\end{array}$

Hence, the remainder will be 1.