Question

Divide (-7x+x^2+15)\(-3+x)

Answer 1

The answer would be x-4+ 3/x-3

Answer 2

The result becomes:

`x-4+(3)/(x-3)`

Explanation:

The given expression in correct order is :

`(x^(2)-7x+15 )/(x-3)`

Now, dividing the leading coefficients of the numerator and divisor we get

`(x^(2) )/(x)=x`

So, quotient is x

Multiplying
`x-3` by x

=>
`x^(2) -3x`

Subtracting
`x^(2) -3x` from
`x^(2) -7x+15` we get
`-4x+15`

This is the new remainder.

Now, the given equation becomes:
`x+(-4x+15)/(x-3)`

Dividing the leading coefficients we get
`(-4x)/(x)=-4`

Multiplying
`x-3` bu -4 to get
`-4x+12`

Subtracting
`-4x+12` from
`-4x+15` = 3

This 3 is the new remainder.

Now, the equation becomes:
`-4+(3)/(x-3)`

Therefore, the result becomes:

`x-4+(3)/(x-3)`