Ccto

1. Multiplying
Polynomials

2. 4 3 2 1 0
In 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.

3. 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!

4. FOIL
F first terms
O outer terms
I inner terms
L last terms

5. (2x-3) (3x+4)
= 2x  3x + 2x 4 + (-3)  3x + (-3) 4
=6x2 + 8x - 9x - 12
=6x2-x-12
Practice:
(5x+3) (4x-6)
20x2 – 30x + 12x – 18
20x2 – 18x - 18

6. 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

7. 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

8. RULE
: 2
2
2
2
)
( b
ab
a
b
a 



You can do this mentally when
you recognize the pattern!
(x+2)2
(x-6)2
x2 + 2x + 2x + 4
x2+4x+4
x2-12x+36

9. Product of the sum and
difference of two terms:
(a+b) (a-b)=a2+ab-ab-b2
=a2-b2
The middle terms cancel out and
you end up with the difference of
perfect squares.
(5x+2) (5x-2)= 25x2-4

10. PRACTICE :
(x+2) (x-2)
(b+6)2
(y-4)2
x2 - 4
b2 + 12b + 36
y2 - 8y + 16