Today's Goals:

Squaring Binomials Dividing a Polynomial by a Binomial

Review Last Khan Academy Topic

03/10/15

Warm-Up:(5)

Complete Class Work 3.8

Notes:

A. Three Polynomial Unit Tests-1. *Polynomial Operations: Adding, Subtracting, Multiplying,

and Dividing polynomials.2. Special Products & Factoring :3. Solving Equations & Advanced Factoring:

* This Friday, March 13, 2015

Warm-Up:

(3xyz - xyz + zx) + (3zyx+ 1) Simplify:

(x + 3)(x + 10 )Use Mental Math to Solve :

(2x + 3)(2x - 3 )(x + 4y)(x - 6y)Use Mental Math to Solve :

(x + y)(x - y )

Squaring a Binomial:

(2x + 3)2 ≠ (4x2 + 9)!! Yesterday we noted that when two (one variable) binomials are multiplied, the result is ALWAYS a trinomial.

The result of (2x + 3)2 must be a trinomial also.

(2x + 3)2 = (2x + 3)(2x + 3) =

This Week's Khan

3rd/4th

Dividing Polynomials

Dividing a Polynomial by a monomial or binomial

Please take complete, easy to read notes, you will need them.

Dividing Polynomials

Part I: Dividing by a Monomial:

1. Since the denominator is the same for each term, divide eachterm in the numerator by the denominator. The result is now a monomial divided by a monomial for each term.

Simplify:2x2

18x4 -10x2 + 6x79x2 -5 + 3x5

Dividing Polynomials

Review: Dividing by a Monomial:Simplify:

#11:

Dividing Polynomials

Part II: Dividing by a Binomial: (Long Division)

We will divide (x3 + x2 - 5x -2) by x-2;

x-2 x3 + x2 - 5x -2

Step 1: Write both in standard form. Then find the highest degree terms in both the divisor and the dividend. In this case, that would be x and x3.

Write these steps in the class notes section of your notebook. You will need it as a guide.

Dividing Polynomials

Step 3: Multiply by the Divisor,

Step 2: Divide x3 by x. The result is: Place above the x2

in the dividend

3x2 - 5x -2Step 4: Subtract, then Repeat the Process: 3x2÷ x =

3x2 - 6xStep 5: Multiply by the Divisor:x - 2

x - 20 Step 6: Last Division

x-2 x3 + x2 - 5x -2

x2

x3 - 2x2

+ 3x + 1

Quick Check. Multiply: (x – 2)(x2 + 3x +1)=

Dividing Polynomials

x-2 x2 - 4 =

Remainder: If there is a remainder, it is shown last as the remainder over the divisor. (Just like regular division)

Solve.

x-2 x2 + 0x1 - 4 Solve.

**Note: If there are missing degrees, fill in with 0x degree

Replace # 5 class work 3.8

Class Work:3.8, Front & Back

Now, factor the result in order to reduce the polynomial to its simplest terms. = 4(x2 + 6x + 9) =4( + )( + ); Can we think of two numbers that when

added, = 6, and when multiplied = 9?4(x+ 3) (x +3); We're back to where we started. These

processes are the opposite of each other.

Squaring a Binomial: