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Factor theorem is the way of finding factor of the polynomial without factorising for example if you have the polynomial 2x^2 -2x +2 and you have to find whether it is divisible by (x+1) or not than put x +1=0 => x=-1 in the given polynomial if the answer is zero than it is divisible otherwise it is not divisible
The factor theorem states that a polynomial has a factor.In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.