The cubic polynomial f(x) is defined by f(x) = 2x^3 -7x^2 +2x+3. Express f(x) in a fully factorised form.
To factorise the equation, we first need to find one of its roots. To do this, we need to find values of x for which f(x)=0.First we will guess x=1.So f(1)=2(13) - 7(12) + 2(1) + 3 = 2-7+2+3=0This tells us that 1 is a root.By algebraic long division, we divide f(x) by x-1 to give f(x)=(x-1)(2x2-5x-3)By guessing again we find that f(3)=0. And by dividing 2x2-5x-3 by x-3 we get 2x2-5x-3 = (x-3)(2x-1).This gives us f(x)=(x-1)(x-3)(2x-1)
