Home » Past Questions » General Paper » Which of the following is a factor of 2 - x - x2?

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 \(f(a)\)

More Past Questions:


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 \(f(a)\)

    Reply
    Like