Question

✴What are:-

▶Factor theorem
▶Remainder theorem

✴What are the differences between factor theorem and remainder theorem?

Answer 1

FACTOR THEOREM-: If p (x) is a polynomial of degree greater thsn or equal to 1 and x-a is a factor of p (x) , then
1 - p(a) is equal to 0
2- if p (a) is ewual to 0 then x-a is a factor of p (x) .
For ex- p (x )=
${x }^{2} - 1$
has a factor x+1 , then p (1) = 0
REMAINDER THEOREM -: If p (x) is a polynomial of degree equal to or greater than 1
and x-a is linear polynomial , then the remsinder is p(a).
For ex. p (x) = x +3
and g (x) = x+1
p (x) ÷ g (x)
= p (-1)

The difference between them is that remainder theorem
helps us to find the remainder but by factor theorem we can say that a polynomial is a factor of another polynomial or not.

Hope it helps.

Answer 2

Answer:

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. The factor theorem states that a polynomial f(x) has a factor if and only if f(k)=0.

In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials. It states that the remainder of the division of a polynomial f(x) by a linear polynomial

Step-by-step explanation:

Factor Theorem is a special case of Remainder Theorem. Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x - a) then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x - a) is a factor of polynomial ƒ(x).