March 10, 2015
Transcript of March 10, 2015
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: