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Suppose the sum is as follows:- use factor theorem to factorise completely x(power3)+x(power2)-4x-4,now first step will be ,let f(x)=x(power3)+x(power2)-4x-4,next step will be, x=2 in (i), we get ,f(2)=2(power3)+2(power2)-4.2-4, next step will be:- 8+4-8-4=0 . next we will right, by factor therom ,x-2 is a factor of f(x) , on dividing x(power3)+x(power2)-4x-4 by x-2< we will get x(power2)+3x+2 as quotient& dividend is0. the other factors of f(x) are the factors of x(power2)+3x+2< after factorising this we will get this factors of the polynomial ,that will be (x-2)(x+1)(x+2)
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N algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial has a factor if and only if (i.e. is a root).
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