1 / 11

The factors of the constant. The factors of the leading coefficient.

The factors of a 0. The factors of the constant. The factors of the leading coefficient. The factors of a n. 1 2. 3 2. The factors of the 12. The factors of the 2. =. 1, 2, 3, 4, 6, 12 1, 2. =. + {1, 2, 3, 4, 6, 12, , }. Example.

hfrancis
Download Presentation

The factors of the constant. The factors of the leading coefficient.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The factors of a0 The factors of the constant. The factors of the leading coefficient. The factors of an 1 2 3 2 The factors of the 12. The factors of the 2. = 1, 2, 3, 4, 6, 12 1, 2 = + {1, 2, 3, 4, 6, 12, , }

  2. Example

  3. Synthetic Division is used to quickly check, if possible rational zeros are factors. Test x = -1. Synthetic division can only be done if the degree of the divisor is 1. x + 1 = 0 1 6 11 6 x = – 1 – 1 – 5 – 6 – 1 1 5 6 0 Move the first number down to the bottom row. Multiply the potential zero to the bottom row number and move the product up to the next column to combine. Repeat the process until you have the remainder at the bottom of the last column.

  4. + + + ++ + + Positive signs + – + –+ – + Alternating signs Zero can be used for any needed sign! ONLY TEST POSITIVE RATIONAL ZEROS! ONLY TEST NEGATIVE RATIONAL ZEROS!

  5. Upper bound Lower bound 2 7 -7 -12 2 7 -7 -12 6 39 96 -4 -6 26 3 2 13 32 84 -2 2 3 -13 14 3 is an upper bound the signs are all positive. -2 is not a lower bound the signs do not alternate. 2 7 -7 -12 -8 4 12 -4 2 -1 -3 0 -4 is not a lower bound, but it is a zero.

  6. Find the zeros of zeros are x-intercepts, soooooo lets graph it! Using the possible rational zero theorem, the smallest number is -6 and the largest is 6. Set your window or Zoom 6. . Count tick marks to make logical guesses! Hit Trace and type in your guess. , x = 1 , x = - ½ Zeros are x = -6

  7. Find the zeros of Zeros are x = 3 , x = -1 , -1 WAIT!! Take another LOOK! It doesn’t cross the x-axis! What does this mean? -1 has even multiplicity. Probably 2. Why? The graph is touching or crossing the x-axis 4 times and with a 5th degree we need at most 5 zeros. . Now we will use the existing 3 rational zeros to find the other 2 zeros that are not rational numbers.

  8. Find the zeros of Zeros are x = 3 , x = -1 , -1 1 3 -10 -22 -7 3 Start by factoring out the two -1 zeros. -1 -2 12 10 -3 -1 1 2 -12 -10 3 0 Remainder -1 -1 13 -3 -1 1 1 -13 3 0 Remainder Now the 3. 3 12 -3 3 1 4 -1 0 Remainder Complete the square Means ZERO

  9. Find the zeros of Zeros are x = 1 , 1 , 1 WAIT!! Take another LOOK! It crosses the x-axis like what type of curve? A Cubic curve. 1 has odd multiplicity. Probably 3. Why? Now we will use the existing 3 rational zeros to find the other 2 zeros that are not rational numbers. The graph is crossing the x-axis in two other locations and with a 5th degree we need at most 5 zeros.

  10. Find the zeros of Zeros are x = 1 , 1 , 1 1 -3 -5 23 -24 8 Start by factoring out all the 1’s. 1 -2 -7 16 -8 1 1 -2 -7 16 -8 0 Remainder 1 -1 -8 8 1 1 -1 -8 8 0 Remainder 1 0 -8 . 1 1 0 -8 0 Remainder Solve for x. Means ZERO

  11. When an x-term is missing, put in a zero to hold the place of the term. c = f(c) 1 0 -12 6 -2 4 16 -2 1 -2 -8 22 = f(-2) 4 1 -2 4 -25 0 -4 3 3 21 -12 -36 3 1 1 7 -4 -12 -40 = f(3)

More Related