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Notes Day 6.3

Notes Day 6.3. Can only divide by x-a. Long Division Synthetic Division Remainder Theorem. Long Division: Divide Factor. x 2. - 1. + 0. Subtract by adding the opposite. 0. - 2x. 0 + 0. X 2 -1. -2x + 3. -2x + 3. Is 3/2 a root?. 0.

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Notes Day 6.3

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  1. Notes Day 6.3 Can only divide by x-a Long Division Synthetic Division Remainder Theorem

  2. Long Division: Divide Factor x2 - 1 + 0 Subtract by adding the opposite 0 - 2x 0 + 0 X2-1 -2x + 3 • -2x + 3 Is 3/2 a root? 0 Yes because there was no remainder!

  3. Long Division: Divide Factor - 5 x + Subtract by adding the opposite -5x - 2 -5x - 20 Is -4 a root? 18 No because there was a remainder!

  4. Synthetic Division: Divide Root 2 3 -4 15 -3 9 -6 -15 0 5 -3 2 Is -3 a root? 2X2-3x+5 Yes because there was no remainder!

  5. Synthetic Division: Divide Root 3 -4 2 -1 -1 7 -3 -9 -10 9 -7 3 3X2-7x+9+ Is -1 a root? No because there was a remainder!

  6. Remainder Theorem -4 1 0 -5 4 12 • 160 16 -4 -44 172 -40 11 -4 1 Find f(-4) Notice f(-4) = the remainder above!!!!!

  7. Remainder Theorem Find P(-1) -1 2 6 -5 0 -61 • -9 -4 -2 9 -70 9 -9 4 2 You can find P(-1) using synth div or substitution

  8. Add To Notes! Not factorable Divide by -1 using synthetic division -1 1 2 -11 -12 Add -1 -1 12 0 -12 1 1 Multiply Factor Now If you can’t factor then QF or compl the square!

  9. Add To Notes! Not factorable Divide by 1 using synthetic division 1 1 4 -3 -2 Add 5 1 2 0 2 5 1 Multiply You can’t factor so QF or complete the square!

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