Question

\[ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0, \]

• A. \(-1\)
• B. \(25\)
• C. \(-36\)
• D. \(48\)

Hint:

Always check quickly by the Remainder Theorem if an integer value might be a root (e.g., \(x=2\)).
- Once factored, match the roots to the given order to evaluate the desired expression.

Answer 1

The Correct Option is A

Step 1: Verify that \(x=2\) is indeed a root.
Substitute \(x=2\) into \(x^5+4x^4-13x^3-52x^2+36x+144\) to check it equals zero. Indeed, it does, so \((x-2)\) is a factor. So \(\boxed{-1}\) is the required sum.