Chapter 8 Worksheet With Answers - Montville Township Public Schools
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38Study Guide and Review - Chapter 8
State whether each sentence is true or false . If false , replace the underlined phrase or expression to
make a true sentence.
2
1. x
+ 5x + 6 is an example of a prime polynomial.
SOLUTION:
The statement is false. A polynomial that cannot be written as a product of two polynomials with integral coefficients
2
is called a prime polynomial. The polynomial x
+ 5x + 6 can be written as (x + 2)(x + 3), so it is not prime. The
2
polynomial x
+ 5x + 7 is an example of a prime polynomial.
2. (x + 5)(x − 5) is the factorization of a difference of squares.
SOLUTION:
The factored form of the difference of squares is called the product of a sum and a difference. So, (x + 5)(x − 5) is
the factorization of a difference of squares. The statement is true.
2
3. (x + 5)(x − 2) is the factored form of x
− 3x − 10.
SOLUTION:
2
(x − 5)(x + 2) is the factored form of x
− 3x − 10. So, the statement is false.
4. Expressions with four or more unlike terms can sometimes be factored by grouping.
SOLUTION:
Using the Distributive Property to factor polynomials with four or more terms is called factoring by grouping because
terms are put into groups and then factored. So, the statement is true.
5. The Zero Product Property states that if ab = 1, then a or b is 1.
SOLUTION:
The statement is false. The Zero Product Property states that for any real numbers a and b, if ab = 0, then a = 0, b
= 0, or a and b are zero.
2
6. x
− 12x + 36 is an example of a perfect square trinomial.
SOLUTION:
Perfect square trinomials are trinomials that are the squares of binomials.
So, the statement is true.
2
7. x
− 16 is an example of a perfect square trinomial.
SOLUTION:
The statement is false. Perfect square trinomials are trinomials that are the squares of binomials.
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