Chapter A.4, Problem 27AYU

To determine

To find: The sum of $a, b,c$ and $d$.

Answer to Problem 27AYU

$-9$

Explanation of Solution

Given:

$\frac{x^3-2x^2+3x+5}{x+2}=a{x}^2+bx+c+\frac{d}{x+2}$

Calculation:

Here the remainder is $-17$ and the quadratic form is $x^2+4x-11=0$.

$a=1, b=-4,c=11$

Therefore $x^2-4x+11+\frac{-17}{x+2}$.

Here $d=-17$.

So the sum of $a, b,c$ and $d=-9$.