Question

Which of these is a factor of $x^3–2x–4$ ​?

• A. True
• B. False
• C. x-2
• D. x-3

Answer 1

The correct option is C x-2

P(1) = $1^3-2\left(1\right)-4=-5$. Hence, when P(x) is divided by (x-1), the remainder will be -5. Hence, $x-1$ is not a factor of the polynomial

P(0) = $0^3-2\left(0\right)-4=-4$. Hence, when P(x) is divided by x, the remainder will be -4. Hence, x is not a factor of the polynomial

P(2)=$2^3-2\left(2\right)-4=0$
This means that when the polynomial is divided by x – 2, the remainder is zero. So, x – 2 is the factor of the polynomial.