Solve Quadratic Equation (x³-4x²+5x-2):(x-1)= x²- 2x-8 | Need Help?

[lion89]

here is my task: (x³-4x²+5x-2):(x-1)=
We did such task in school but I didn't got it ..

Here is the task that we did in school
(x³-3x²-6x+8) :(x-1)= x²- 2x-8 but I don`t get it why x² is the result and why 3x² ??
Can someone help me? Thank you in advance

 

[symbolipoint]

Regular polynomial division is easier than standard long division with pure constants. Your approach should be exactly the same.

Ask this: What is x^3 divided by x ? It is certainly not three times anything. You have no reason for coming to 3*x^2.

 

[HallsofIvy]

To expand on symbolipoint's response, suppose you were asked to divide 3524232 by 83. You would start by noting that 8 divides into 35 for times so the first digit of the quotient is (probably) 4. you need the "probably" because the digit after the 8 might cause a problem. But in this case 4*83= 329 and 352- 329= 23, less than 83. So you subtract those and your problem becomes 234232 divided by 81. 8 will divide into 23 twice (3*8= 24 so 3 times doesn't quite fit). 2*83= 163 and 234- 163= 71. You know that the first two digits of the quotient are 42.. and you continue.

x³- 3x²- 6x- 8 divided by x-1 is much the same thing- the "x" just represents a number so all the rules of algebra apply. x divides into x³ x³/x= x^{2[/sup times so we try x2 as the divisor: x2 times x-1 is x3- x2 and x3- 3x2 minus x3- x2 is -3x2- (-x[sup[2})= -2x². Of course, the x³ terms cancel- that was the whole point of choosing the divisor to be x². We now have left -2x²- 6x+ 8 to be divided by x- 1.

x² will divide into -2x² -2x times, so we try -2x as the next term in the quotient: -2x times x- 1 is -2x²+ 2x and -2x<sup>2- 6x minus -2x2+ 2x is just -6x-(2x)= -8x. We have left -8x+ 8 to be divided by x- 1.

Okay, -8x divided by x is, of course, -8 and -8 times x-1 is -8+ 8, exactly what we had left: x-1 divides into -8x+ 8 exactly -8 times. Putting all of that together, x-1 divides into x3- 3x2+ 6x- 8 exactly x2-2x -8 times.

Now, you try exactly the same thing with x3- 4x2+ 5x- 2 divided by x-1. Warning: even when you are dividing numbers, divisions don't always come out even: 33 divided by 4 is 8 with a remainder of 1 (or 8+ 1/4).</sup>