1 / 5

Pre-AP Algebra 2

Pre-AP Algebra 2. Goal(s): Divide polynomial expressions using synthetic division Apply the remainder and factor theorems. Polynomial Synthetic Division. Synthetic Division can be used when: Your divisor is LINEAR Your divisor has a leading coefficient of 1 Examples: x+3, x-5, x-12, x+99

smithsam
Télécharger la présentation

Pre-AP Algebra 2

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. Pre-AP Algebra 2 • Goal(s): • Divide polynomial expressions using synthetic division • Apply the remainder and factor theorems

  2. Polynomial Synthetic Division • Synthetic Division can be used when: • Your divisor is LINEAR • Your divisor has a leading coefficient of 1 • Examples: x+3, x-5, x-12, x+99 • You will use the coefficients of the dividend only • Because you are dividing by a linear divisor, the degree of your quotient will decrease by 1 compared to your original polynomial

  3. Polynomial Synthetic Division • Synthetic Division: • Write coefficients only inside upside-down division bar (leave a blank line under them) • Remember to “placehold” any missing terms with a 0 • Write the zero outside the bar (remember, if you’re given a factor of (x-k), k is the zero) • Bring down the first term • Multiply and then add subsequent terms • The final sum is your remainder

  4. Divide polynomial expressions • Synthetic Division Example:

  5. Remainder & Factor Theorems • Remainder Theorem: • If polynomial f(x) is divided by (x-k) then the remainder, r, =f(k) • Because the remainder in the previous example was -21, when x=-2, f(x)=-21 • Factor Theorem: • A polynomial f(x) has (x-k) as a factor if f(k)=0 • Because f(-2)=-21 in the previous example, (x+2) is not a factor of 3x5-8x3+2x2-x+1

More Related