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Math Help - Factorising this polynomial?

  1. #1
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    Factorising this polynomial?

    How to divide this polynomial, f(x) = x^3 - 2x^2 + x - 2 with x -1 by using long division? I got stuck at -x^2 + x because after that, the remainder is 0 but there is still the -2 remaining. However, the solution is x^2 + 1. How?
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  2. #2
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    Quote Originally Posted by mark1950 View Post
    How to divide this polynomial, f(x) = x^3 - 2x^2 + x - 2 with x -1 by using long division? I got stuck at -x^2 + x because after that, the remainder is 0 but there is still the -2 remaining. However, the solution is x^2 + 1. How?
    That's because the solution is incorrect. Dividing x^3 - 2x^2 + x - 2 by x - 1 gives you a quotient of x^2 - x with a remainder of -2.

    Maybe you meant that you want to divide x^3 - 2x^2 + x - 2 by x - {\color{red}2}? Because if you do that, you do get a quotient of x^2 + 1. You sure you copied the problem down correctly?


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  3. #3
    Super Member dhiab's Avatar
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    Quote Originally Posted by mark1950 View Post
    How to divide this polynomial, f(x) = x^3 - 2x^2 + x - 2 with x -1 by using long division? I got stuck at -x^2 + x because after that, the remainder is 0 but there is still the -2 remaining. However, the solution is x^2 + 1. How?
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mark1950 View Post
    How to divide this polynomial, f(x) = x^3 - 2x^2 + x - 2 with x -1 by using long division? I got stuck at -x^2 + x because after that, the remainder is 0 but there is still the -2 remaining. However, the solution is x^2 + 1. How?

    Use the rational zeros theorem to determine possible roots of the function.
    When you have them, make use of the fact that if x=c is a root of f(x), then x-c is a factor of the polynomial function f(x). when you have found all factors x=c, then divide.

    Possible zeros. 1,-1,2,-2.
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