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The work shows the first steps of writing a partial fraction decomposition. StartFraction negative 5 x cubed + 2 x squared + 9 x + 2 Over (x squared + 2) squared EndFraction = StartFraction A x + B Over x squared + 2 EndFraction + StartFraction C x + D Over (x squared + 2) squared EndFraction Negative 5 x cubed + 2 x squared + 9 x + 2 = (A x + B) (x squared + 2) + C x + D Negative 5 x cubed + 2 x squared + 9 x + 2 = A x cubed + 2 A x + B x squared + 2 B + C x + D For this partial fraction decomposition, find the unknowns. A = , B = , C = , and D =

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kingdukkwashere

Answer:

I'm certainly late, but it took me a while to figure this one out so I want to leave an answer.

A=-5 B=2 C=19 D=-2

Step-by-step explanation:

I looked back at the video and actually tried to pay attention and the way to figure these problems out is set up all of the degrees of x in an equation. So, take all of the coefficients that are attached to an x^3, and set them up equal to each other. This makes -5=A, which is the first answer. Repeat for x^2 and you have B=2. For x, it becomes 9=2A+C. A is equal to -5 (from the x^3), so you can substitute and get c=19. Repeat for the x^0 term (the constants), and you get 2=2B+D. Plug in the value for B, 2, and get 2=4+D, which then becomes D=-2. That's how you get the answer and I hope this helps somebody.

The values are A=-5, B=2, C=19 and D=-2

What is partial fraction?

Partial fractions are the fractions used for the decomposition of a rational expression. When an algebraic expression is split into a sum of two or more rational expressions, then each part is called a partial fraction. Hence, basically, it is the reverse of the addition of rational expressions.

Given:(-5x³+2x²+9x+2) / x²+2 =(Ax + B)/x²+2 + (Cx + d)/x²+2 .......(1)

First, we have to perform the long division as follows

The long division gives

(-5x³+2x²+9x+2 )/ x²+2= ( -5x+2)+ (19x-2)/ x²+2

Now, we have to find the partial fraction for  (19x-2)/ x²+2

But, as denominator cannot be factored, So no partial fraction can be calculated.

Thus, (-5x³+2x²+9x+2 )/ x²+2=  ( -5x+2)+ (19x-2)/ x²+2

Comparing it with equation (1), we get

Hence, A=-5, B=2, C=19 and D= -2

Learn more about partial fraction here:

https://brainly.com/question/23125414

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