Question

can anyone tell me what is factor theorem . class 9 ch 2 ( I want explanation only)​

Answer 1

Answer:

if g(x) is a factor of polynomial p(x) then p(x) is completely divisible by g(x)

Answer 2

Step-by-step explanation:

What is a Factor Theorem?

Factor theorem is commonly used for factoring a polynomial and finding the roots of the polynomial. It is a special case of a polynomial remainder theorem.

As discussed in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the methods to do the factorisation of a polynomial.

Proof

Here we will prove the factor theorem, according to which we can factorise the polynomial.

Consider a polynomial f(x) which is divided by (x-c), then f(c)=0.

Using remainder theorem,

f(x)= (x-c)q(x)+f(c)

Where f(x) is the target polynomial and q(x) is the quotient polynomial.

Since, f(c) = 0, hence,

f(x)= (x-c)q(x)+f(c)

f(x) = (x-c)q(x)+0

f(x) = (x-c)q(x)

Therefore, (x-c) is a factor of the polynomial f(x).

How to Use Factor Theorem

The steps are given below to find the factors of a polynomial using factor theorem:

Step 1 : If f(-c)=0, then (x+ c) is a factor of the polynomial f(x).

Step 2 : If p(d/c)= 0, then (cx-d) is a factor of the polynomial f(x).

Step 3 : If p(-d/c)= 0, then (cx+d) is a factor of the polynomial f(x).

Step 4 : If p(c)=0 and p(d) =0, then (x-c) and (x-d) are factors of the polynomial p(x).

If you find it difficult to do this theorem, there is another theorem called remainder theorem.

Hope you understand

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