Fibonacci Haiku: Julian

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SP#5: Unit J Concept 6- Repeating Factors in Fraction Decomposition

PART ONE: Remember whatever you mulitply to the denominators to get CD, multiply it to its numerator as well which will be in letter (ABC). When you set it equal to the original equation, remember to put the value of 0 if there isn't any for that term.

PART TWO: Combine like terms! Set it into a system and cancel out the x's and x^2's. Use elimination to solve for a variable (in this case, eliminate A and C in rows 2-3 to find B. After finding B, plug it into row 1 to find A, and then plug in A & B in row 3 to solve for C. Notice that when we plug in the numbers to the corresponding letters, the second equation was not there because the value of B was 0.

PART THREE: Check your answers! From the resulting equation we found from the previous step, do the same thing and find the CD and remmeber to mulitply whatever you did at the bottom to the numerator as well. Combine like terms and you should end up with the origial equation you had in the very beginning and you're done! :- )

SP#4: Unit J Concept 5- Partial Fraction Decomposition with DF

Part 1: COMPOSING. We need to get a common denominator for all three equations by multiplying the bottom of each denominator by the other denominators. After doing this, don't forget to multiply the numberators by it as well! After you get the numerators, combine like terms and put it over the common denominator (which does not need to be FOILED out). That will be your composed equation!

Part 2: To start decomposing, set your equation to A/x+5 + B/x+2 +C/x-7. Do the same thing you did to get common denominators and also for your numerators. (Notice you'll have letters in your equation now!) Set it equal to the numerator we found in the previous part. Combine like terms again and cross off the x^2 and x's to make it a lot easier!

Part 3: Plug in the coefficients into your matrix. After you have that plugged in, find the rref. Your resulting answer should be as shown above. Notice that A=4, B=2, and C=3! It lines up with the equations from the two earlier steps! 

We have successfully decomposed the equation back to its original equation after we composed it! :- ) 

SV#5 - Unit J Concepts 3-4: Matrices

Don't be scared when you look at this problem! It's actually really easy even though it's a lot of work! (HENCE MY 8 MINUTE VIDEO, SORRY ABOUT THAT) Be sure to simplify equations when you can so you can make your life so much easier when add/subtracting! Remember, our goal is to get our matrix to be in the Row- Echelon form. This means there will a right triangle of 0's and a staircase of 1's! Follow the Gaussian Elimination and you'll be in good hands. Remember that if you have a consistent dependent, solve until the very end in the matrix even if it means you'll have 2 rows left. Be sure to plug in the value of each letter correctly to ensure an accurate answer at the end.