7
(xn+2-1)/(x2-1)
x3 - 2x2 + x - 2 =(x - 2)(x2 + 1)
(x+1)(x+5)(x+2)
The inverse of a number is 1 divided by that number. So the inverse of x3 + 1 is 1/(x3 + 1).
The factors of x^3 - x^2 + 2 are (x + 1) and (x^2 - 2x + 2)
lim (x3 + x2 + 3x + 3) / (x4 + x3 + 2x + 2)x > -1From the cave of the ancient stone tablets, we cleared away several feet of cobwebs and unearthed"l'Hospital's" rule: If substitution of the limit results in ( 0/0 ), then the limit is equal to the(limit of the derivative of the numerator) divided by (limit of the derivative of the denominator).(3x2 + 2x + 3) / (4x3 + 3x2 + 2) evaluated at (x = -1) is:(3 - 2 + 3) / (-4 + 3 + 2) = 4 / 1 = 1
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
The quotient is: x^2 +2x +3
4
x3 - x2 + x - 2 has no rational factors.
(x - 1)(x^2 - 5)
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)