2# Long Division Polynomials

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Presentation transcript:

2# Long Division Polynomials

Teaching note Show video Long Division vs. Synthetic Division Show students what they are working towards

Common Core objectives: * Students will be able to use long division to divide polynomials by other polynomials. Use synthetic division to divide polynomials by binomials of the form (x – k). Use the Remainder Theorem and the Factor Theorem. * Teacher will instruct students to learn about the process of division. Learn about a couple of theorems to help in factoring and solving higher level polynomials

Polynomials vocabulary Synthetic Division 1. 2. 3. Long Division 1. 2. Graphic Organizer vocabulary Division of Polynomials Synthetic Division 1. 2. 3. Long Division 1. 2. 1. 2. 3. 4.

vocabulary Roots Zeros Rational Root Theorem Remainder Theorem Due Test Day Roots Zeros Rational Root Theorem Remainder Theorem Factor Theorem Synthetic Division Prime Factors vocabulary

What does it mean to factor a number into its prime factors? 90 462 what times what equals …

Simple Division 3x y z + 12xyz – 4xy z yesterday 3x y z + 12xyz – 4xy z 3xyz 3 2 3 2 Simple Division 3x y z + 12xyz – 4xy z 3 2 3 2 3xyz 3xyz 3xyz

Long Division is very similar to Polynomial Division

Long Division 18 8 6 5 2597 3 3 2597 5 9 7 -( ) 24 1 9 -( ) 1 7 -( ) Will 3 go into 2? NO 2597 3 3 2597 5 9 7 -( ) 24 Will 3 go into 25? YES 1 9 -( ) 18 1 7 -( ) 15 2

Polynomial Division 3x+13x -5x +10x - 3 -( ) -( ) -2x +4 3x +1x - -7 3x+1 2 -2x +4 x 3 2 3x+13x -5x +10x - 3 3 2 -( ) 3x +1x - 2 -6x + 10x Look at 1st term 2 3 -( ) + -6x - 2x + 3x( ?? ) = 3x x2 12x - 3 -( ) 12x + 4 - -7

example Think Think Think Multiply: 6x2(x – 2). Subtract.

Polynomial Division Notice that there is no x term. However, we need to include it when we divide.

Polynomial Division -( ) -( ) -( )

Try This Answer:

*****application Long Division worksheet Due next class