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how to answer this one : (x^4-4x^3-22x^2+100x-75) divided by (x^2-4x+3)


Sagot :

The answer is x^2-25. You can check it by multiplying the answer by the divisor.
 Hope it helps.
Factor the numerator (using rational zero theorem, then factor by grouping)
(x-1) ( x+5) (x-5) (x-3)

Factor the denominator:
(x-1) (x-3)

Rewrite:
(x-1) (x+5) (x-5) (x-3)    
  (x-1)(x-3)

= (x+5) (x-5) or x² - 25