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- Hey, do you know what we are doing in class today?
- Oh, I wasn't even paying attention to that!
- Well, if you read the board, you'll know that we're learning how to do case 4
- Decomposition of N(x)/D(x): Case 4
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- Class, please quiet down
- Wait, how do you know what equations are case 4?
- Case 4: decompose P/Q where Q has repeated irreducible quadratic factors
- If the equation has a repeated, irreducible quadratic factor, then it is a case 4 equation
- The least common denominator is: (x^2 + 2)^2.You would break up the equation and multiply it by the LCD:Ax+B/(x^2 +2) plus Cx+D/(X^2+2)^2
- The first step of solving a case 4 equation is multiplying the equation by its LCD.
- For example: 1) -4x^2 - 13/ X^4 + 4x^2 + 4
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- -4x^2-13 = Ax^3+Bx^2+2Ax+ 2B+Cx+D
- BElieve THEre is GOOD in the world
- One you do that, you add the two equations and you will get:
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- For C, you will combine 2A + C and set it equal to 0. 2A+C=02(0)+C=0C=0
- For B, because it is similar to the first coefficient in the numerator, it will equal -4
- BElieve THEere is GOOD in the world
- Because A doesn't have any similar coefficients, it will equal 0
- Then, you will equate the coefficients!
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- BElieve THEere is GOOD in the world
- For D, you will combine 2B+D and set it equal to -13 from the first equation:2B+D=-13
- Once you plug in the value of B you will get:2(-4)+D=-13-8+D=-13D=-5
- And that is how you do case 4, see it's not that difficult
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