Question

find the quotient when (x^3-6x^2+2x+8) is divided by (x-3)​

Answer 1

Here x^2 -3x -7 is quotient and -13 is remainder

Answer 2

The quotient when $(x^3-6x^2+2x+8)$ is divided by (x-3)​  is $x^2 -3x -7$ and -13 is remainder.

Step-by-step explanation:

Given:

$(x^3-6x^2+2x+8)$ is divided by (x-3).

To Find:

The quotient when $(x^3-6x^2+2x+8)$ is divided by (x-3)​.

Solution:

As given, $(x^3-6x^2+2x+8)$ is divided by (x-3).

$x^3-6x^2+2x+8 = x^3-3x^2-3x^2+9x-7x+21-13$

                            $= x^{2} (x-3)- 3x(x-3)-7(x-3)-13$

                            $= (x-3) (x^{2} - 3x-7)-13$

Therefore,

$\frac{(x^3-6x^2+2x+8)}{(x-3)} =\frac{(x-3) (x^{2} - 3x-7)}{(x-3)} -\frac{13}{(x-3)}$

                      $= (x^{2} - 3x-7) -\frac{13}{(x-3)}$

Thus, the quotient when $(x^3-6x^2+2x+8)$ is divided by (x-3)​  is $x^2 -3x -7$ and -13 is remainder.

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