Question

Please Help me On this And explain please show ur work

Answer 1

You don't even have to actually do the division to find the correct answer.

The leading term of q(x) is x³/x² = x, so only the 1st and 3rd selections are appropriate.

The remainder r(x)/b(x) will have the divisor as b(x), so only ...
.. the 1st selection is appropriate.

Answer 2

This can be done using long division that we have learned with numbers, except that each digit in the numeric long division is replaced with a number that can exceed 10.

Thus we can write the division as where the right most digit represent a number, and each number to the left represent an increasing power of x.
                 ________________________
1 +2 +1    |  1   +10   +13     + 39

We will use a first quotient digit of 1 and begin the division

                 _1______________________
1 +2 +1    |  1   +10   +13     + 39
                   1     +2     +1                                   (subtract)

                            8     12      39


After that, we have a multiplier of 8 and continue

                 _1___8___________________
1 +2 +1    |  1   +10   +13     + 39
                   1     +2     +1                                   (subtract)

                            8     12      39
                            8     16        8                         (subtract)

                                    -4      31

This means that we have a quotient of (x+8) with a remainder of -4x+31
thus the final expression looks like

$\frac{x^3+10x^2+13x+39}{x^2+2x+1}=x+8+\frac{-4x+31}{x^2+2x+1}$