Question

Review the work showing the first few steps in writing a partial fraction decomposition. (NEED IT DONE IN LESS THAN 10 MINS PLEASE!)

Answer 1

ANSWER:

C.

A = 2

8A + B = 15

16A + 4B + C = 19

STEP-BY-STEP EXPLANATION:

We have the following expression:

$\frac{2x^2+15x+19}{\left(x+4\right)^3}$

We apply the partial fraction decomposition as follows:

$\begin{gathered} 2x^2+15x+9=\frac{A}{x+4}+\frac{B}{(x+4)^2}+\frac{C}{(x+4)^3} \\ \\ 2x^2+15x+9=A(x+4)^2+B(x+4)+C \\ \\ 2x^2+15x+9=Ax^2+8Ax+16A+Bx+4B+C \\ \\ Ax^2=2x^2\rightarrow A=2 \\ \\ 8Ax+Bx=15x\rightarrow8A+B=15 \\ \\ 16A+4B+C=19 \end{gathered}$

Therefore, the correct answer is C.

A = 2

8A + B = 15

16A + 4B + C = 19