Question

ne proof of the theorem
1.A) Select the correct alternative answer and write it
0) In A ABC, 2B. 52º and mcc72°, then mais
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Answer 1

Answer:

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).

Another Method

By 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.

(x-c) exactly divides f(x)

Therefore, f(c)=0.

The following statements are equivalent for any polynomial f(x)

The remainder is zero when f(x) is exactly divided by (x-c)

(x-c) is a factor of f(x)

c is the solution to f(x)

c is a zero of the function f(x), or f(c) =0