Question

\(f(x)=5x^4-9x^3-3x^2+11x-18\) is divided by \((x-2)\) then the remainder is

• A. 0
• B. -7
• C. 7
• D. 1

Answer 1

The Correct Option is A

By the \(\textbf{Remainder Theorem}\), the remainder when \( f(x) \) is divided by \( x - a \) is \( f(a) \).
Here, we divide by \( x - 2 \), so we compute \( f(2) \):
\[ f(2) = 5(2)^4 - 9(2)^3 - 3(2)^2 + 11(2) - 18 \] \[ = 5(16) - 9(8) - 3(4) + 22 - 18 \] \[ = 80 - 72 - 12 + 22 - 18 \] \[ = (80 - 72) = 8,\quad (8 - 12) = -4,\quad (-4 + 22) = 18,\quad (18 - 18) = 0 \]

The correct answer is option (A): \(0\)