The table represents the start of the division of 3x^4+22x^3+37x^2-7x+10
by the indicated divisor

The quotient is x^3 + 4x^2 -x + 1.

Solution:
By polynomial grid division, we start by the divisor 3x + 10 placed on the column headings.
               3x      10
     x^3    3x^4   

We know that 3x^4 must be in the top left which means that the first row entry must be x^3. So the row and column multiply to 3x^4. We use this to fill in all of the first row, multiplying x^3 by the terms of the column entries.
                 3x       10
     x^3      3x^4   10x^3 
     4x^2

We now got 10x^3 though we want 22x^3. The next cubic entry must then be 12x^3 so that the overall sum is 22x^3.
                  3x         10
     x^3      3x^4     10x^3 
     4x^2    12x^3

Now we have 40x^2, so the next quadratic entry must be -3x^2 so that the overall sum is 37x^2.
                 3x          10
     x^3      3x^4      10x^3 
     4x^2    12x^3    40x^2
     -x       -3x^2      -10x

This time we have -10x, so the next linear entry must be 3x so that the overall sum is 7x.
                 3x          10
     x^3      3x^4     10x^3 
     4x^2    12x^3    40x^2
     -x         -3x^2    -10x
     1           3x         10

The bottom and final term is 10, which is our desired answer. Therefore, we can now read the quotient off the first column:
     3x^4+22x^3+37x^2-7x+10 / 3x + 10 = x^3 + 4x^2 -x + 1

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.