Multiplying Polynomials

4 3 2 1 0In addition to level 3, students make connections to other content areas and/or contextual situations outside of math.

 

Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features. - Factor using methods including common factors, grouping, difference of two squares, sum and difference of two cubes, and combination of methods. - Add, subtract, and multiply polynomials, - Explain how the multiplicity of the zeros provides clues as to how the graph will behave. - Sketch a rough graph using the zeros and other easily identifiable points.

Students will factor polynomials using limited methods, perform operations (excluding division) on polynomials, and identify key features on a graph. - Add and subtract polynomials. - Multiply polynomials using an area model. - Factor polynomials using an area model. - Identify the zeros when suitable factorizations are available. - Identify key features of a graph.

Students will have partial success at a 2 or 3, with help.

Even with help, the student is not successful at the learning goal.

Focus 9 Learning Goal – (HS.A-SSE.A.1, HS.A-SSE.A.2, HS.A-SEE.B.,

HS.A-APR.A.1, HS.A-APR.B.3, HS.A-REI.B.4) = Students will factor polynomials using multiple methods, perform operations (excluding division) on polynomials and sketch rough graphs using key features.

1. 5x(3x2-2x+1) (give the 5x to each term)

5x(3x2)+5x(-2x)+5x(1)

15x3-10x2+5x

2. 6x2(5x2+3x-9)

30x4+18x3-54x2

Simple multiplication:Distribute monomial to all terms!

FOIL

F first terms

O outer terms

I inner terms

L last terms

(2x-3) (3x+4)

= 2x 3x + 2x 4 + (-3) 3x + (-3) 4

=6x2 + 8x - 9x - 12

=6x2-x-12Practice:

(5x+3) (4x-6)

20x2 – 30x + 12x – 18

20x2 – 18x - 18

Distributive Property

(x-2)(5+3x-x2)

=x(5+3x-x2)+(-2)(5+3x-x2)

=5x + 3x2 - x3 – 10 - 6x + 2x2

=-x + 5x2 - x3 - 10 (put in order)

=-x3+5x2-x-10

Special Products:Square of a binomial

(a+b)2= a2+ab+ab+b2

= a2+2ab+b2

(a-b)2 =a2-ab-ab+b2

=a2-2ab+b2

RULE: 222 2)( bababa You can do this mentally when you recognize the pattern! (x+2)2 (x-6)2

x2 + 2x + 2x + 4x2+4x+4

x2-12x+36

Product of the sum and difference of

two terms:(a+b) (a-b)=a2+ab-ab-b2

=a2-b2The middle terms cancel out and you end up with the difference of perfect squares.

(5x+2) (5x-2)=25x2-4

PRACTICE :

(x+2) (x-2)

(b+6)2

(y-4)2

x2 - 4

b2 + 12b + 36

y2 - 8y + 16