Question

Divide (x^3-8x^2+17x-10)/(x-5)

Answer 1

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, $\frac{x^{3}-8x^{2}+17x-10}{x-5}$ = (x - 2)*(x - 1)