Factoring Algebra 2

Question

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

Answer 1

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)

Answer 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).

Answer 3

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)