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Topics in Calculus: Activity #1
Algebra Review
Directions: For each of the topics below, work in groups to solve the problems. Use the
examples and hints to help you, and be sure to ask questions if you need help!
Simplifying Expressions
Combining “Like” Terms. Each part of a polynomial that is separated by addition or
subtraction is called a term. One way to simplify a polynomial expression is to group terms that
are similar (have the same type of variable) and add/subtract the coefficients (numbers in front of
the variables).
Example:
Group “like” terms
Add/Subtract coefficients
Order the terms from highest
degree to lowest
Multiplying Polynomials. Distribute by multiplying each term in the first multiplier by each
term in the second multiplier. (Even though it doesn’t always work, remember FOIL?)
Example:
Distribute the terms
Combine like terms
Raising to a Power. The exponent indicates how many times you need to multiply the
expression in the parentheses by itself. When simplifying an expression by a power, try writing
the statement as a multiplication problem instead.
Example:
University of Northern Colorado 2
Topics in Calculus: Activity #1
Complex Fractions. When the numerator or denominator are fractional polynomials, you may
want to use the technique below. Multiply the numerator by the reciprocal (multiplicative
inverse) of the denominator.
Example:
Multiply by the reciprocal
Multiply across
Now you try: Simplify the following expression.
1)
2)
3)
4)
5)
6)
7)
8)
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Topics in Calculus: Activity #1
Factoring Polynomials
Common Term Factoring. The first step to factoring a polynomial is to check if any of the
terms have something (a factor) in common. Be sure to check both the coefficients and the
variables for commonalities.
Example:
Put the common term out front and
divide each original term by it
Simplify
Factoring Quadratics. Consider the general case:
. Let m and n be a factor pair
of A, p and q be a factor pair of B, and s and t be a factor pair of C. You want to factor the
quadratic,
, such that
.
Example:
Check!
Now you try: Factor the following polynomials.
9)
10)
11)
12)