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Answer:
This is because it helps us factorize the polynomial more easily.
Step-by-step explanation:
The remainder theorem which states that if P(x) is a polynomial and x - a is a linear factor, then the remainder when P(x) is divided by x - a is P(a). When P(a) = 0, then x - a is a factor of P(x).
So, the remainder theorem is used to determine whether a linear binomial is a factor of a polynomial because it helps us factorize the polynomial more easily.
When the polynomial is divided by the linear factor, we obtain a polynomial of lesser degree which can then be further factorized to obtain all the factors of our initial polynomial.
The remainder theorem is used to determine the factors of a polynomial, and also to determine the remainder of a polynomial when it is divided by a linear binomial
A linear binomial is represented as:
[tex]\mathbf{f(x) = mx \pm c}[/tex]
Where n and x are both constants
A polynomial is represented as:
[tex]\mathbf{P(x) = ax^n +......+d}[/tex]
Assume the linear binomial is:
[tex]\mathbf{f(x) = x - c}[/tex]
If f(x) is a factor of P(x), then by the remainder theorem, the following must be true
[tex]\mathbf{P(c) = 0}[/tex]
This is so, because it allows factorization to be done with ease.
However, if [tex]\mathbf{P(c) \ne 0}[/tex]
Then, f(x) is not a factor of P(x)
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