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

C. on edg

Explanation:

2023 precalc

Answer 2

C.

A = 2

8A + B = 15

16A + 4B + C = 19

Explanation:

We have the following expression:

`(2x^2+15x+19)/(\left(x+4\right)^3)`

We apply the partial fraction decomposition as follows:

`\begin{gathered} 2x^2+15x+9=(A)/(x+4)+(B)/((x+4)^2)+(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