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