Answer:
-2
Explanation:
We'll have to solve the problem first, the strategy used here is to divide the first term of the dividend by the first term of the divisor (x^4 / x) which is x^3 and then we add it as the first term in the quotient, and then multiply x^3 by the divisor ( x^3 * (x-3)) which is x^4 - 3x^3, then we subtract the x^4 - 3x^3 from the dividend ( ( x^4 + 2x^3 - 10x^2 - 4x - 35 ) - ( x^4 - 3x^3 ) ) which is equal to 5x^3 - 10x^2 - 4x - 35, and we do the last steps over and over until the remainder equals -2, in case of confusion, here are the other steps:
5x^3 / x = 5x^2
the current quotient = x^3 + 5x^2
5x^2 * x-3 = 5x^3-15x^2
( 5x^3 - 10x^2 - 4x - 35 )-( 5x^3-15x^2 ) = 5x^2 - 4x - 35
5x^2 / x = 5x
the current quotient = x^3 + 5x^2 + 5x
5x * x-3 = 5x^2-15x
( 5x^2 - 4x - 35 ) - ( 5x^2-15x ) = 11x - 35
11x / x = 11
the final quotient = x^3 + 5x^2 + 5x + 11
11 * x-3 = 11x - 33
(11x - 35) - (11x - 33) = -2
So, the remainder will be -2