Question

The work shows the first steps for writing a partial fraction decomposition.



Which equations can be used in a system of equations to solve for the unknowns. Check all that apply.

A = 0
xxxB = 0
xxxxD = –5
xxxxA + C = 0
2A + 2B = 4
it's B C D the three in the middle

Answer 1

Answer:

B C D

Step-by-step explanation:

Answer 2

Partial fraction decomposition involves breaking down algebraic fractions into smaller piece.

The equations that can be used are:

$\mathbf{B = 0}$   ,   $\mathbf{D= -5}$   and    $\mathbf{A + C = 0}$

From the question. we have:

$\mathbf{4x^3 - 5 = 2Ax^3 +Ax + 2Bx^2 + B + Cx + D}$

Collect like terms

$\mathbf{4x^3 - 5 = 2Ax^3 + 2Bx^2 +Ax + Cx + B + D}$

Compare both sides, using the power of x

$\mathbf{4x^3 = 2Ax^3}$

$\mathbf{- 5 = B + D}$

$\mathbf{0 = 2Bx^2 }$

$\mathbf{0 =Ax + Cx }$

Divide both sides of $\mathbf{4x^3 = 2Ax^3}$ by 2x^3

$\mathbf{A = 2}$

Divide both sides of $\mathbf{0 = 2Bx^2 }$ by 2x^2

$\mathbf{B = 0}$

Divide both sides of $\mathbf{0 =Ax + Cx }$ by x

$\mathbf{A + C = 0}$

Substitute $\mathbf{B = 0}$ in $\mathbf{- 5 = B + D}$

$\mathbf{D= -5}$

Hence, the equations that can be used are:

$\mathbf{B = 0}$  

$\mathbf{D= -5}$ and

$\mathbf{A + C = 0}$

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