Question

Define Factor theorum and Remainder theorum.

Answer 1

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.

Remainder Theorem

Consider the polynomial g(x) of any degree greater than or equal to one and any real number c. If g(x) is divided by a linear polynomial (x-c), then the remainder is equal to g(c).

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hope this answer helps you

Answer 2

Here is the answer to your question!!

FACTOR THEOREM

If p(x) is a polynomial of degree > 1 and p(a) = 0

Then ( x -a) is a factor of p (x)

If p(-a) = 0

Then (x+a) is a factor of p(x).

REMAINDER THEOREM.

If p(x) is a polynomial of degree >1 and when we divide p(x) by (x+a), we get remainder = p(-a).

If we divide p(x) by (x-a) , we get remainder = p(a).

Hope it helped!!