1. The document provides steps for factoring polynomials, simplifying binomials, multiplying monomials and binomials, finding areas of rectangles with variable sides, naming polynomials, and other algebra concepts. It includes examples and explanations for each topic. 2. Methods are given for factoring polynomials by finding the greatest common factor or using the difference of squares formula. Binomials should be squared by writing them twice and using FOIL, not squaring individual terms. 3. To multiply a monomial by a polynomial, the term outside is distributed to each term inside. FOIL is used to multiply binomials. Perimeters can be found by doubling the total length and width given in an area formula.

1. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
1. Explain how to factor a polynomial
such as 5x3+20x2+10x
First find the GCF of the numbers and
variables. Then write the GCF outside
the parenthesis. Inside the parenthesis,
figure out what is needed to be
multiplied by the GCF to get the new
polynomial.
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2. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
2. Explain how to factor a polynomial
such as x2+18x+80. How do you know
when to factor this way instead of
finding the GCF?
The factored form will look like this:
(x + ___)(x + ____). Find two numbers that
multiply to 80 and add to 18 and fill them
in.
You can factor this way as long as the first
term is something squared with no extra
numbers (example: x2 but not 5x2
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3. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
3. How do you simplify a binomial that
is being squared?
Example: (5x+3)2
What is the incorrect way to simplify
these kinds of expressions?
Write the binomial twice (to square it)
and FOIL or distribute to simplify.
Incorrect way is to square the 5x and the
3 and get 25x2 + 9
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4. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
4. Explain the steps to multiply a
monomial by a polynomial like the one
below:
5x2(2x3+6x+3)
Take the term on the outside and
distribute it to every term on the inside.
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5. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
5. Explain the process for multiplying
two binomials like the ones below:
(2x ­ 4)(5x + 6)
Use the FOIL method or distributive
method to first multiply 2x by everything
in the second binomial, and then multiply
­4 by everything in the second binomial.
Make sure to simplify any like terms!!!
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6. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
6. Make a drawing showing that a
square with sides of x length has been
increased on one side by 2 and
increased on the other side by 3.
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7. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
7. Picture a square with sides of x feet.
The length is increased by 5, and the
width is decreased by 5. Write the
steps you would take to find a
comparison between the original
square's area and the new rectangle's
area.
Hint: Challenge 5
See Challenge 5 for full explanation on
how to create a table to compare the
two areas.
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8. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
8. Given the equation a = l(40 ­ l),
which represents the area of a
rectangle, explain how you can figure
out the perimeter of the rectangle.
The 40 in the problem represents
the length and width added together.
Since there are two lengths and two
widths in a rectangle, double 40 to
get the whole perimeter: 80.
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9. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
9. Explain how you can find the
maximum area of a rectangle by using:
1. a graph
2. a table
Draw examples to support your
explanation.
On a graph, the maximum area is the
highest point of the parabola. On a
table, the maximum is the number that
is the highest in the graph.
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10. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
10. Explain how to name polynomials
and give names for the following
polynomials:
3x2 + 4x + 6
10x + 3
2x4 ­ 3x2 + 5x + 9
See Challenge 1 for complete instructions. You name a
polynomial based on how many terms it has (monomial,
binomial, trinomial, polynomial) and based on the highest
exponent it has (0=constant, 1= linear, 2= quadratic, 3=
cubic, 4 and higher is just a 4th degree, 5th degree, etc.
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11. Unit 3A Assessment_Review_Study Guide Creation.notebook December 17, 2012
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