Question

Name the remainder for the quotient and describe or show how you found theremainder.

Answer 1

We are going to use long division to found the remainder

`x^3-x^2-17x-15(1)/(x-5)^{}^{}`

Find an expression that multiplies by x-5, we can cancel the x^3, we use the same sign because when we pass to operate the sing change, like this:

x^2(x-5) = x^3-5x^2

Now, x^3 - x^2

-x^3+5x^2

--------------------

0 +4x^2

`4x^2-17x-15(1)/(x-5)`

Find an expression to cancel 3x^2 using the dividend x-5:

4x(x-5)= 4x^2 -20x

Operate:

4x^2 -17x

-4x^2 +20x

------------------

0+3x

Find an expression to cancel 3x

`3x-15(1)/(x-5)`

3(x-5)= 3x-15

Operate:

3x-15

-3x+15

-------------

0

So , the remainder is 0

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