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# Which of the following is a factor of 2 - x - x2?

### Question

Which of the following is a factor of 2 - x - x2?

### Options

A) 1 - x

B) 1 + x

C) x - 1

D) 2 - х

The correct answer is C.

### Explanation:

At $$x = 1, 2 - x - x^2 = 0$$
i.e. $$f(x) = 2 - x - x^2$$
$$f(1) = 2 - 1 - 1^2 = 2 - 2 = 0$$
Therefore $$(x - 1)$$ is a factor of $$2 - x - x^2$$
According to the factor theorem, when a polynomial is divided by any of its factors, it leaves a remainder of zero.
According to Remainder's theorem, the remainder can be obtained by equating the divisor to zero and substituting into the given polynomial, thus, if $$x - a$$ is a factor of $$f(x)$$, the remainder when $$f(x)$$ is divided by $$x - a$$ is $$f(a)$$

## Dicussion (1)

• At $$x = 1, 2 - x - x^2 = 0$$
i.e. $$f(x) = 2 - x - x^2$$
$$f(1) = 2 - 1 - 1^2 = 2 - 2 = 0$$
Therefore $$(x - 1)$$ is a factor of $$2 - x - x^2$$
According to the factor theorem, when a polynomial is divided by any of its factors, it leaves a remainder of zero.
According to Remainder's theorem, the remainder can be obtained by equating the divisor to zero and substituting into the given polynomial, thus, if $$x - a$$ is a factor of $$f(x)$$, the remainder when $$f(x)$$ is divided by $$x - a$$ is $$f(a)$$

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