Question

Please give the solution.

Answer 1

"here is solution"

"hope helps "

Answer 2

Given f(x) = 2x^4 - 5x^3 + 2x^2 - x + 2.

Given g(x) = x^2 - 3x + 2

                = x^2 - 2x - x + 2

               = x(x - 2) -(x - 2)

               = (x - 1)(x - 2).

If (x - 1) and (x - 2) are the factors of f(x), then f(x) is divisible by g(x).

Now,

If f(1) = 0 and f(2) = 0 then f(x) is divisible by g(x).

(i)

f(1) = 2(1)^4 - 5(1)^3 + 2(1)^2 - 1 + 2

    = 2 - 5 + 2 - 1 + 2

    = 6 - 6

    = 0.    

(ii)

f(2) = 2(2)^4 - 5(2)^3 + 2(2)^2 - 2 + 2

     = 32 - 40 + 8 - 2 + 2

     = 0.

From (i) & (ii), f(1) = 0 and f(2) = 0.

Therefore, f(x) is exactly divisible by x^2 - 3x + 2.

Hope this helps!