We can do this two ways: polynomial division or synthetic division.
Polynomial division involves factoring the equations first. Synthetic division is basically long division.
I'm opting for polynomial division cause it's shorter.
First, we factor ((x^4)-(x^3)-(7x^2)+4x-3).
((x^4)-(x^3)-(7x^2)+4x-3)=(x-3)((x^3)+(2x^2)-x+1)
Then divide:
((x-3)((x^3)+(2x^2)-x+1)) ÷ (x-3) = (x^3)+(2x^2)-x+1
So your answer is B
What is the expression ????
1 and 5 are equal, 1 and 8 are equal, 5 and 8 are equal
So if 1+5=100 and they're equal divide by 2: 100/2=50. So if 1 and 5 equals 50, then 8 also =50 :)
8
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Option C: 
The last two terms given of the standard polynomial are:

This shows 2 patterns to us:
r 's degree is increasing per term in the given polynomial.
s 's degree is decreasing per term in the given polynomial.
The sum of powers of variates r and s is 2+4 = 3+3 = 6.
And since standard polynomial, the same pattern must be present in all terms of the series.
All options except C are not valid.
Option C has term
for which r's degree plus s's degree is 1 + 5 = 6.
And r's degree 1 < s's degree 5.
Thus its a valid term to be putted as first term in standard form of polynomial in consideration.
Thus Option C:
is the needed expression.
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