Answer:
(x - 2)*(x - 1) is the answer
Step-by-step explanation:
We have to divide the polynomial f(x) = x^{3}-8x^{2}+17x-10 by (x-5).
Now, after dividing f(x) gets simplified into (x-5)*(x^{2}-3x+2).
So, we need to factorize the quadratic equation x^{2}-3x+2.
i.e. x^{2} - 3x + 2 = x^{2} - x - 2x + 2 = x(x-1) - 2(x-1) = (x - 2)*(x - 1)
Therefore, f(x) again gets simplified into (x-5)*(x - 2)*(x - 1)
Now eliminating the common factor (x-5).
We get, [tex]\frac{x^{3}-8x^{2}+17x-10}{x-5}[/tex] = (x - 2)*(x - 1)
