**Monday**

*NWEA*

**Tuesday**

*NWEA*

**Wednesday**

*NWEA*

*Classwork:* Review worksheet (Kuta)

**Monday**

*NWEA*

**Tuesday**

*NWEA*

**Wednesday**

*NWEA*

*Classwork:* Review worksheet (Kuta)

**Monday**

*NWEA*

**Tuesday**

*NWEA*

**Wednesday**

*NWEA*

*Classwork:* Review worksheet (Kuta)

A supermutation is a number that contains all the possible permutations of a set of digits. For instance, 123121321 contains all the possible permutations of 1, 2, and 3 (123, 132, 213, 231, 312, and 321). This video is an interesting exploration of permutations, beyond what we’re doing in class.

Powerpoints: Feb 2 Feb 1 Jan 31 Jan 30 Jan 29

**Monday**

*Topic:* Fundamental Counting Theorem and Permutations

**Tuesday**

*Topic:* Fundamental Counting Theorem and Permutations

*Classwork:* 11-1 G Side 1

**Wednesday**

*Topic:* Permutations and Combinations

*Classwork:* Kuta Worksheet (Permutations)

**Thursday**

*Topic:* Combinations

*Classwork:* Kuta Worksheet (Combinations)

**Friday**

*Topic:* Combinations

Powerpoints: Feb 2 Feb 1 Jan 31 Jan 30 Jan 29

**Monday**

*Topic:* Fundamental Counting Theorem and Permutations

**Tuesday**

*Topic:* Fundamental Counting Theorem and Permutations

*Classwork:* 11-1 K Side 1

**Wednesday**

*Topic:* Permutations and Combinations

*Classwork:* Kuta Worksheet (Permutations)

**Thursday**

*Topic:* Combinations

*Classwork:* Kuta Worksheet (Combinations)

**Friday**

*Topic:* Combinations

In class and in the book, it is said that synthetic division only works if the divisor is a linear function, i.e., something that can be written in the form (x + k). That’s not true, but synthetic division with higher-order polynomials is a little more complicated.

Here’s an example of synthetic division using a linear divisor. Consider \((3x^3 + 2x^2 – x + 7)\div (x – 2)\). Here it is using synthetic division: \[\begin{array}{cccccc}2&|&3&2&-1&7\\&|&\downarrow&6&16&30\\&&——&——&——&——\\&&3&8&15&37\end{array}\]

The quotient is \(3x^2 + 8 + 15 + \frac{37}{x – 2}\).

Synthetic division for higher order divisors relies on the same concept, but needs a new line for each coefficient. For instance, a quadratic divisor uses two lines instead of one; a cubic divisor uses three lines; and so on.

For instance, \((x^2 + 3x – 7)(x^2 – 5x + 2) = x^4 – 2x^3 -20x^2 + 41x – 14\). To get a remainder, we’ll change the last two terms. To the left, we’ll reverse the signs of both of the coefficients of the lower terms of the divisor; as before, we’ll write all of the coefficients of the dividend: \[\begin{array}{cccccccc}-3&7&|&1&-2&-20&40&-10\\ & &|&\downarrow&-3&15&-6& \\ & &|&\downarrow&&7&-35&14\\ & & &——&——&——&——&——\\ & & &1&-5&2&-1&4\end{array}\]

In the second row, we use opposite of the coefficient from the \(x\) term (that is, -3) as a multiplier; in the third row, we use opposite of the constant (that is, 7).

This gives us a result of \(x^2 – 5x + 2 + \frac{-x + 4}{x^2 + 3x – 7}\), which is the same thing we get from long division.

Notice that, regardless, the lead coefficient (\(a\)) of the divisor must be 1. You can use synthetic division with, say, a divisor of \(4x – 5\), but you’d have to use \(x – 5/4\) instead, and then divide each coefficient of the result by 4.

For example, consider \((2x^3 + x^2 – 17x + 14)/(2x + 7)\). This is what synthetic division yields: \[\begin{array}{cccccc}-7/2&|&2&1&-17&14\\&|&\downarrow&-7&21&-14\\&&——&——&——&——\\&&2&-6&4&0\end{array}\]

The actual quotient is \(x^2 – 3x + 2\), with no remainder, which is what we get from dividing each of the resulting values by 2.

The Study Packet is worth points! Make sure to turn it in!

All papers **must be** turned in by Friday, January 26, before I leave the building. I will be finalizing grades over the weekend. Any papers turned in after Friday will not count.

Powerpoints: None

**Monday**

*Study for midterms*

*Classwork:* Study packet

**Tuesday**

*Study for midterms*

*Classwork:* Study packet

**Wednesday**

*Midterm (hours 1 and 2)*

**Thursday**

*Midterm (hour 4)*

**Friday**

*Midterm (hours 5 and 6)*