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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