Question

what is meant by factor therom

Answer 1

Factor Theorem  Let f (x) be a polynomial. If a polynomial f (x) is divided by x = c, then the remainder will be zero. That is, x = c is zero or root of a polynomial f (x) , which also makes (x – c) is a factor of f (x). Thus, the theorem states that if f (c)=0, then (x–c) is a factor of the polynomial f (x). The converse of this theorem is also true. That is, if (x – c) is a factor of the polynomial f (x), then f(c)=0.  Proof of factor theorem:  Consider a polynomial f (x) which is divided by (x – c) .  Then, f (c) = 0.  Thus, by the Remainder theorem,  Thus, (x – c) is a factor of the polynomial f (x).  Proof of the converse part:  By the Remainder theorem,  f (x) = (x – c) q(x) + f (c)  If (x – c) is a factor of f (x), then the remainder must be zero.  That is, (x – c) exactly divides f (x).  Thus, f (c) = 0.  Hence proved.

Answer 2

✔✔heya here is ur answer!!!!

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Factor theorem: If p(x) is a polynomial of degree n>=1 and a is any real number, then (i) x-a is factor of p(x) , if p(a) =0 (ii) and its converse "if (x-a) is a factor of a polynomial p(x) then p(a) = 0

Note:

p(x) = ax^3+bx^2+cx+d and (x-1) is a factor of p(x)

=> p(1) = 0

=> a+b+c+d = 0

i.e. the sum of the coeffiecients of a polynomial is zeeo then (x-1) is a factor...

THANK YOU ✌✌

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