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Assignment, red pen, pencil, highlighter, GP notebook

Learn how to factor higher degree trinomials using the same method as factoring quadratics. Practice factoring and graphing polynomial functions. Review fractions and rational expressions.

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Assignment, red pen, pencil, highlighter, GP notebook

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  1. Assignment, red pen, pencil, highlighter, GP notebook M3D6 Have out: Bellwork: State the degree of each function, identify the leading coefficient, and find the zeros: 1) y = x3 – 4x2 2) y = 2x2 – 10x + 12 x3 – 4x2 = 0 2x2 – 10x + 12 = 0 2(x2 – 5x + 6) = 0 x2(x – 4) = 0 2(x – 2)(x – 3) = 0 x2 = 0 x – 4 = 0 x – 2 = 0 x – 3 = 0 x = 0 x = 4 x = 2 x = 3 3 2 Degree:________ Leading coefficient:________ Zeros:________ Degree:________ Leading coefficient:________ Zeros:________ +1 +2 x = 0, 0, 4 x = 2, 3

  2. Factoring Higher Degree Trinomials Factoring higher degree trinomials is very similar to the method we use when factoring quadratics Let’s review what we have done since Algebra 1: Example: Factor the quadratic 8 2 4 6

  3. 8 6 Example: Factor the trinomial Trinomials such as can also be written in quadratic form as Ex: These trinomials can be factored as the product of two binomials. Split x4 into x2 and x2. These will be the first terms in the binomials. 2 4 Ex: If you are unsure of your answer, use F.O.I.L. or a generic rectangle to check your answers.

  4. -18 5 6 -3 12 -8 Practice: a) b) 1 -6 5 3 c) -6 -2

  5. Recall from yesterday: Even degree + leading coefficient Even degree – leading coefficient Odd degree + leading coefficient Odd degree – leading coefficient

  6. Or remember it this way: Even Degree, raise the roof!

  7. Odd Degree, Saturday Night Fever!

  8. Graphing Polynomial Functions, Part 2 Determine the following information for each polynomial function. Graph the function. 1. y = (x – 4)(x + 3) 0 = (x – 4)(x + 3) x – 4 = 0 x + 3 = 0 x = 4 x = –3 Be sure to plot the y–intercept, too! x = -3, 4 (0, –12) zeros: _____________ 2 +1 degree: ____ leading coefficient: an = ________ Endpoint behavior: (choose one)

  9. 2. y = –x(x – 3)(x + 3) 0 = –x(x – 3)(x + 3) –x = 0 x – 3 = 0 x + 3 = 0 x = 0 x = 3 x = –3 Odd degree, so down then up. Wait, the L.C. is negative! x = –3, 0, 3 zeros: _____________ end behavior: ________ 3 –1 degree: ____ leading coefficient: an = ________

  10. 3. y = (x + 3)2(x + 1) (0, 9) 0 = (x + 3)2(x + 1) (x + 3)2 = 0 x + 1 = 0 x + 3 = 0 x = –1 x = –3 x = –3, –3, –1 zeros: _____________ end behavior: ________ 3 +1 degree: ____ leading coefficient: an = ________ double tangent With a _______ factor, the polynomial is ________ to the x–axis at the _____________. x–intercepts

  11. Try exercises #4 on your own.

  12. 4. y = x(x + 1)(x – 2) 0 = x(x + 1)(x – 2) x = 0 x + 1 = 0 x – 2 = 0 x = –1 x = 2 x = –1, 0, 2 zeros: _____________ end behavior: ________ 3 1 degree: ____ leading coefficient: an = ________

  13. 5. y = –2x2(x – 1) (x + 1) –2x2 = 0 x – 1 = 0 x + 1 = 0 x = 0 x = 1 x = –1 Bounce! x = –1, 0, 0, 1 zeros: _____________ end behavior: ________ 4 –2 degree: ____ leading coefficient: an = ________ Skip #6 and #7 for right now. You need to finish these tonight. Let’s go to #8.

  14. 8. y = x(x – 3)3 x = 0 (x – 3)3 = 0 x – 3 = 0 x = 3 triple zero! At this zero, the graph will curve like a cubic. 0, 3, 3, 3 zeros: _____________ end behavior: ________ 4 +1 degree: ____ leading coefficient: an = ________

  15. 6. y = (x – 3)2(x + 1)2 (x – 3)2 = 0 (x + 1)2 = 0 x – 3 = 0 x + 1= 0 (0, 9) x = 3 x = –1 Bounce! x = –1, –1, 3, 3 zeros: _____________ end behavior: ________ 4 1 degree: ____ leading coefficient: an = ________

  16. 7. y = –2(x – 2)(x + 3)2(x – 1) x – 1 = 0 x –2 = 0 (x + 3)2 = 0 x = 1 x = 2 x + 3 = 0 x = –3 Bounce! (0, –36) x = –3, –3, 1, 2 zeros: _____________ end behavior: ________ 4 –2 degree: ____ leading coefficient: an = ________

  17. Summary: When we graph a polynomial function, 1. Determine and graph the _________. (y = __ ) ( _________ if necessary.) 2. Graph the _________. (x = __ ) 3. Find and graph the ________ behavior 4. Remember, the polynomial function is __________ to the x–axis for any ________ zeros. 5. Graph the rest of the polynomial. zeros 0 Factor y–intercept 0 endpoint tangent double

  18. Old slides

  19. 6. y = (x – 3)2 + 2 locator point: 0 = (x – 3)2 + 2 (3, 2) –2 = (x – 3)2 No solution?! We’ll have to use our “imagination” to address this later. None zeros: _____________ end behavior: ________ 2 +1 degree: ____ leading coefficient: an = ________

  20. Fractions Add to your notes: Baby Math Review How to multiply fractions: Multiply straight across. 6 2 How to divide fractions: Flip the second fraction. 1 5 Change the sign to multiplication. Multiply across.

  21. Rational Expressions Add to your notes: Take out the rational expressions worksheet. Let’s do problems #2 and #8. 3 3 We can simplify since everything is multiplied. 2) 4 2 Multiply across and simplify.

  22. Rational Expressions Add to your notes: 8) Flip the second fraction. Change the sign to multiplication. (m + 1)(m + 1) 10(m – 1) 2 Simplify and multiply across.

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