Question

hi guys.

explain about factor theroum?


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Answer 1

Step-by-step explanation:

If f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then

★(x-a) is a factor of f(x), if f(a)=0

★Its converse “ if (x-a) is a factor of the polynomial f(x), then f(a)=0”

Example:

Consider the polynomial function f(x)= x2 +2x -15

The values of x for which f(x)=0 are called the roots of the function. By solving the equation, f(x)=0

Then, we get

x2 +2x -15 =0

(x+5)(x-3)=0

(x+5)=0 or (x-3)=0

x = -5 or x = 3

Because (x+5) and (x-3) is a factor of x2 +2x -15, -5 and 3 are the solutions to the equation x2 +2x -15=0, we can also check as follows:

If x = -5 is the solution , then

f(x)= x2 +2x -15

f(-5) = (-5)2 + 2(-5) – 15

f(-5) = 25-10-15

f(-5)=25-25

f(-5)=0

If x=3 is the solution, then;

f(x)= x2 +2x -15

f(3)= 32 +2(3) – 15

f(3) = 9 +6 -15

f(3) = 15-15

f(3)= 0

If the remainder is zero, (x-a) is a polynomial of f(x)

Answer 2

Answer:

FACTOR THEORM:- If p(x) is a polynomial of degree $n \geqslant 1$and a is any real number, then

(i) x-a is a factor of p(x), if p(a) =0, and

(ii) p(a)=0, if x-a is a factor of p(x).

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