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Factoring Algebra 2

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3 Answers

x^4 - x^3 + 8x - 8

= x^3(x-1) + 8(x-1), grouping

= (x^3+8)(x-1)

= (x+2)(x^2-2x+4)(x-1), using the sum of two cubes formula: a^3+b^3 = (a+b)(a^2-ab+b^2)

 As a rule , anytime coefficients of a polynomial add up to 0, the polynomial has root of X=1, or polynomial has factor of ( X -1 ).  That polynomial can be , by long division be divided by X -1.
 
   Here are grouped in such a way that factoring by grouping , the (X -1) can be extracted. 
  
    By as a general rule like:
 
      2 X5 - 3X4 + 5X3+3X2 -5X - 2 , where  ( 2 -3 + 5 + 3 - 5 -2 = 0) can be , by long division, be divided by ( X -1).

You can also combime x4 and 8x and x3 with 8. You can write

                                   x4 -x3 +8x - 8 = x(x3 +8) - (x3 +8) = (x-1)(x3 +8) = (x-1)(x+2)(x2 -2x +4)

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