The work shows how to use long division to find (x2 + 3x –9) ÷ (x – 2). what will be the remainder over the divisor?

Hey!

The first step to solving the rest of this problem would be to distribute the parenthesis in -( 5x - 10 ).

Original Equation :
-( 5x - 10 )

New Equation {Changed by Distributing the Parenthesis} :
- ( 5x ) - ( -10 )

Now we'll simplify the equation.

Old Equation :
- ( 5x ) - ( -10 )

New Equation {Simplified} :
-5x + 10

Okay, now that that part of the equation has been changed, we can add the simplified part to our entire equation.

New Equation :
5x - 9 - 5x + 10

Next we need to group like terms.

Old Equation :
5x - 9 - 5x + 10

New Equation {Changed by Grouping Like Terms} :
5x - 5x - 9 + 10

And now we add the similar elements.

Old Equation :
5x - 5x - 9 + 10

New Equation {Changed by Grouping Like Terms} :
-9 + 10

And finally we simply add the numbers.

Old Equation :
-9 + 10

Solution {Old Equation Solved} :
1

So, this means that 5x - 9 - ( 5x - 10 ) is  1.

Hope this helps!

- Lindsey Frazier ♥