Question

What should be added to x^3-2x^2-3x-4 so it is completely divisible by x^2-x?

Answer 1

Click the above picture of the solution.

Answer 2

Answer:

4x+4 is added to the polynomial $x^{3} -2x^{2} -3x -4$ completely divisible by $x^{2} - x$

Step-by-step explanation:

Given: The polynomial function is $x^{3} -2x^{2} -3x -4$

To find: To check the polynomial function is completely divisible by $x^{2} - x$

Solution:

The given polynomial function $x^{3} -2x^{2} -3x -4$ divisible by $x^{2} - x$

Rule of divisibility:

Mathematicians use a set of specific rules called the "divisibility rules" to determine whether a given integer is divisible by a certain number or not.

Calculation:

               x-1

           ________________

$x^{2} - x$)  $x^{3} -2x^{2} -3x -4$

      (-)   $x^{3} - x^{2}$

        _________________

.                 - $x^{2}$ $-3x$

              (-)$-x^{2} +x$

        ___________________

                        -4x  -4

We get the quotient (x-1) and the remainder (-4x-4)

Here we use the concept of rule of divisibility

$x^{3} -2x^{2} -3x -4$ is divisible by $x^{2} - x$

Quotient = (x-1)

Remainder =  (-4x-4)

Therefore we have to add 4x+4 to the polynomial $x^{3} -2x^{2} -3x -4$

So if 4x+4 is added it is completely divisible by $x^{2} - x$

Final answer:

4x+4 is added to the polynomial $x^{3} -2x^{2} -3x -4$ completely divisible by $x^{2} - x$

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