# Remainder Theorem Calculator

The calculator will calculate $f(a)$ using the remainder (little Bézout's) theorem, with steps shown.

Enter a polynomial:

Enter the point a:

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## Solution

Your input: find $f\left(3\right)$ for $f\left(x\right)=x^{3} - x^{2} + 2 x + 7$.

According to the remainder theorem, $f(a)$ is the remainder from dividing $f(x)$ by $x-a$.

Thus, to find $f\left(3\right)$, find the remainder from dividing $x^{3} - x^{2} + 2 x + 7$ by $x - 3$.

For this, use the synthetic division calculator.

The remainder is $31$, therefore, $f\left(3\right)=31$.

Answer: $f\left(3\right)=31$.