Question

Please Help me On this And explain
please show ur work

Answer 1

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


`(x^3+10x^2+13x+39)/(x^2+2x+1)=x+8+(-4x+31)/(x^2+2x+1)`

Answer 2

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.