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Given that f(x)=2x33x211x+6 and \(f(3) =...

Given that f(x)=2x33x211x+6 and f(3)=0, factorize f(x)

A.

(x - 3)(x - 2)(2x + 2)

B.

(x + 3)(x - 2)(x - 1)

C.

(x - 3)(x + 2)(2x -1)

D.

(x + 3)(x - 2)(2x - 1)

Correct answer is C

Since f(3) = 0, then (x - 3) is a factor of f(x).

Dividing f(x) by (x - 3), we get 2x2+3x2.

2x2+3x2=2x2x+4x2

x(2x1)+2(2x1)=(x+2)(2x1)

Therefore, f(x)=(x3)(x+2)(2x1)