Dividend: 4x^4 -x^2 +17x^2 +11x +4 Divisor: 4x +3 Quotient: x^3 -x^2 +5x -1 Remainder: 7
Divide by x: x(x2 - 20x + 19); = x(x -1)(x - 19)
The integral of -x2 is -1/3 x3 .
x3 -3x2 -x - 1 divided by x+2 equals x2-5x+9 remainder -19 It's difficult to show how to work it out on this computer but division with algebra has a lot in common with doing long division with integers.
By x3 I assume that you mean x3. In which case f(x)=x3-2x+1, and f'(x)=3x2-2. Therefore our iteration formula is: xn+1=xn- (xn3-2xn+1)/(3xn2-2) Starting with x0=0 we get: x1=0.5 x2=0.6 x3=0.617391304 x4=0.618033095 x5=0.618033988 x6=0.618033988 Starting with x0=0.9 we get: x1=1.065116279 x2=1.009457333 x3=1.000255451 x4=1.000000195 x5=1 x6=1 Starting with x0=-1.5 we get: x1=-1.631578947 x2=-1.618183589 x3=-1.618034007 x4=-1.618033989 x5=-1.618033989 The 3 real roots to f(x) are x=-1.618033989, x=0.618033988, and x=1
x3 + x2 + 4x + 4 = (x2 + 4)(x + 1)
x3 + x2 - 6x + 4 = (x - 1)(x2 + 2x - 4)
x2(x3 + 1) is the best you can do there.
x3 + 1 = (x + 1)(x2 - x + 1) The x + 1's cancel out, leaving x2 - x + 1
(xn+2-1)/(x2-1)
3 - 3x + x2 - x3 = (1 - x)(x2 + 3)
(x + 4) / (x3 - 11x + 20) = (x + 4) / (x2 + 4x - 5)(x + 4) = 1 / (x2 + 4x - 5) = 1 / (x + 5)(x - 1), where x ≠ -4
x4 - 1.We can not "solve" this as we have not been told the value of x. However, we can simplify this expression:We have an x and a minus x here which will cancel out. Likewise the x2 and x3 will cancel out with the -x2 and -x3 respectively. This therefore leaves us with just x4 - 1.
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - x + 1)
The integral of 1 + x2 is x + 1/3 x3 + C.
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
x3+3x2+3x+2 divided by x+2 equals x2+x+1