Question

Review the work showing the first few steps in writing a partial fraction decomposition.

Answer 1

Answer:

$A = 2$

$B = -1$

$C = -9$

Step-by-step explanation:

Given

$2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C$

Required

Find A, B and C

Rearrange the expression

$2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C$

$2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C$

To do this, we simply compare the expressions on both sides of the equation.

So, we have:

$Ax\² = 2x\²$ --- (1)

$8Ax + Bx = 15x$ --- (2)

$16A + 4B + C = 19$ --- (3)

Divide both sides by x² in (1)

$Ax\² = 2x\²$

$A = 2$

Divide both sides by x in (2)

$8Ax + Bx = 15x$

$8A + B = 15$

Substitute 2 for A.

$8*2 + B = 15$

$16+ B = 15$

Make B the subject

$B = 15 - 16$

$B = -1$

Substitute 2 for A and -1 for B in (3)

$16A + 4B + C = 19$

$16*2 + 4*-1 + C = 19$

$32 - 4 + C = 19$

$28 + C = 19$

Make C the subject

$C = 19 - 28$

$C = -9$

Answer 2

Answer:

Option-3

Step-by-step explanation:

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