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Notes Day 6.4

Notes Day 6.4. R ational Root Theorem Find roots of polynomial equations. Notes 6.4 R ational Root Theorem. q. p. Possible Rational Roots:. 4. 3. ±1, ±3. ±1,±2,±3,±4,±6,±12. Pairs!. 2. 4. 0. 3. 1.

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Notes Day 6.4

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  1. Notes Day 6.4 Rational Root Theorem Find roots of polynomial equations

  2. Notes 6.4 Rational Root Theorem q p PossibleRational Roots:

  3. 4 3 ±1, ±3 ±1,±2,±3,±4,±6,±12 Pairs! 2 4 0 3 1 When given polynomial equations to solve, you will use the solving methods you learned in the quadratics unit , synthetic division and the rational root theorem! Sometimes the given problem is factorable and you can find roots… but if it is not, you will have to list possible rational factors and then guess and try synthetic division to find a factor. Then you will solve the remaining quotient equation.

  4. Notes 6.4 Rational Root Theorem Solve! This problem is factorable!

  5. Not factorable Guess a root and do 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!

  6. Not factorable Rewrite this fcn on your notes! Pick one and do synthetic division 1 1 -6 11 -6 -5 1 6 0 6 -5 1 These numbers are the a, b, and c now Factor Now If you can’t factor then QF or compl the square!

  7. If no root was given you would have to list possible rational roots and guess a root by doing synthetic division until one of the possible roots has a remainder of zero! 3 1 -9 27 -27 -18 3 27 0 9 -6 1 Factor Now If you can’t factor then QF or compl the square!

  8. Factored form: f(x)=(x-3)(x-3)(x-3) Roots: Set factors equal to zero and solve Max # of Turns: Degree minus 1 ….TWO turns max End behavior right: Left: Down Up Leading coefficient positive Odd so opposite left and right end behaviors X-intercept(s) Real roots Y-intercept: (0 , -27) Sub in zero for x and solve for y

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