You can work this out with long division, by checking to see if (x2 - 1) is a factor of (2x4 + 4x3 - x2 + 4x - 3). It is. Unfortunately, the WikiAnswers system is somewhat limited in depicting things such as long division, so we won't be able to represent it here. In short though, (2x4 + 4x3 - x2 + 4x - 3) / (x2 + 1) is equal to 2x2 + 4x - 3. which means that:
(x2 + 1) / (2x4 + 4x3 - x2 + 4x - 3)
= (x2 + 1) / (x2 + 1)(2x2 + 4x - 3)
= 1 / (2x2 + 4x - 3)
2x4
(x2 + 14 + 48 / (x + 8) = (x2 + 62) / (x + 8) =(x2 + 8x - 8x - 64 + 126) / (x + 8) = x - 1 + 126/(x+8)
x2 + x2 = 2x2
x3 + 1 = (x + 1)(x2 - x + 1) The x + 1's cancel out, leaving x2 - x + 1
(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).
The numerical coefficient of it is 2 .
Quotient: 2x3-x2-14x+42 Remainder: -131 over (x+3)
3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =(12 + 15 + x2 -5)/x2 =(27 - 5 + x2)/x2 =(22 + x2)/x2
4x3 + 16x2 - 180x = 4x(x2 + 4x - 45) = 4x(x + 9)(x - 5)
i got 42 divided 7x
4x(x2 - 2)
Given 3x3 + 4x2 +x + 7 is divided by x2 + 1, find the results:
2x4
5
2x4 - 7x3 + x2 + 7x - 3 = (x + 1)(2x3 - 9x2 + 10x - 3) = (x + 1)(x - 1)(2x2 -7x + 3) = (x + 1)(x - 1)(x - 3)(2x -1)
formula for the midpoint of a line
If you mean: f(x) = x4 - 3x3 + 5x2 / x2 then: f(x) = x4 - 3x3 + 5 ∴ f'(x) = 4x3 - 9x2 If you mean: f(x) = (x4 - 3x3 + 5x2) / x2 then: f(x) = x2 - 3x + 5 ∴ f'(x) = 2x - 3