Question

is a factor of $x^3–2x–4$.

• A. $x–1$
• B. $x–2$
• C. $x–3$
• D. $x–4$

Answer 1

The correct option is B $x–2$

According to factor theorem, $x–a$ is a factor of a polynomial P($x$), if P($a$) = 0.
Given P($x$) = $x^3–2x–4$.
Hence, P(1) = $1^3–2\times 1–4$ = -5,
P(2) = $2^3–2\times 2–4$ = 0,
P(3) = $3^3–2\times 3–4$ = 17,
P(4) = $4^3–2\times 4–4$ = 52.
So, ($x–2$) is a factor of $x^3–2x–4$.