262139
The remainder is 8. (x2 + 4)/(x - 2) = (x + 2) + 8/(x - 2) or x2 + 4 = (x - 2)(x + 2) + 8
(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
21.8621
0.0893
74 divided by 5 equals 14 with a remainder of 4
-3
The remainder is 8. (x2 + 4)/(x - 2) = (x + 2) + 8/(x - 2) or x2 + 4 = (x - 2)(x + 2) + 8
(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
6x3+29x2-40x-42 divided by 6x+5 Quotient: x2+4x-10 Remainder: 8
Answer is x2 -6x+14 with remainder 2
58
59
2519
29
To find the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ), we can use polynomial long division. Upon performing the division, we find that the remainder is a polynomial of degree less than the divisor, which is ( x^2 + x + 1 ). The result shows that the remainder is ( -x + 1 ). Thus, the remainder when ( x^3 + 1 ) is divided by ( x^2 + x + 1 ) is ( -x + 1 ).
57