How do I use the remainder theorem to divide 2x^2-5x-1 by x-3?

1 Answer
Oct 9, 2014

The remainder theorem results in the output value of the given polynomial after evaluating it at a specific value of $x$.

First you solve the divisor by setting it equal to zero.

$x - 3 = 0$
$x = 3$

This $3$ will be used to multiply each coefficient of the of the polynomial.

The coefficients of $f \left(x\right) = 2 {x}^{2} - 5 x - 1$ are $2 , - 5 , \mathmr{and} - 1$.

We begin by multiplying the value of $x$, which is $3$, by the first coefficient.

This product is then added to the next coefficient. The result of the previous operation is then multiplied by $3$ and we continue until we reach last coefficient by repeating the steps above.

The numbers in parentheses are are the coefficients.

$3 \cdot \left(2\right) = 6$

$\left(- 5\right) + 6 = 1$

$3 \cdot \left(1\right) = 3$

$\left(- 1\right) + 3 = 2$

By using the remainder theorem we see that $f \left(3\right) = 2$

Please see the video below for another example.