<p>Let <span>\(\frac{x + 2}{x^2 + x - 6} = \frac{Ax^4 + Bx^3 + Cx^2 + Dx + E}{x^2 + x - 6}\)</span>, the value of <span>\(5A + 4B + 3C + 2D + E\)</span> is equal to</p>
Step-by-Step Solution
Key Concept: Express the numerator as a polynomial and use partial fractions or direct comparison to find coefficients A, B, C, D, E.
<p>First simplify the left side: <span>$\frac{x+2}{(x+3)(x-2)} = \frac{x+2}{x^2+x-6}$</span>. Therefore the numerator on the right must equal x+2, giving us coefficients. Then evaluate at the given linear combination.</p>
Correct Answer: D