Question

use division algorithm to find the quotient and remainder for f(x) = x^4-3x^3-5x^2+21x-14 and g(x)=x^2-7

Answer 1

GIVEN
P (x) = x^4 - 3x^3 - 5x^2 + 21x - 14 and
g(x)=x^2 - 7

q(x) = x^2-3x+2
__________________________
x^2-7) x^4 -3x^3-5x^2+21x-14(
_____x^4____ -7x^2
____-________+____
_______- 3x^3+2x^2+21x -14
_______-3x^3_____+21x
_______+________-___
____________2x^2____-14
____________2x^2____-14
____________-________+__
_____________XXXXXXXXX

Therefore, Quotient = x^2-3x+2 and remainder is zero.