Mid-Chapter Quiz
Determine whether each expression is a polynomial. If so, identify the polynomial as a monomial,
binomial, or trinomial.
2
1. 3y − 2
SOLUTION: A polynomial is a monomial or the sum or difference of monomials, so the expression is a polynomial.
The expression has two terms, so it is a binomial.
5
2
2. 4t + 3t + t
SOLUTION: A polynomial is a monomial or the sum or difference of monomials, so the expression is a polynomial. The
expression has three terms, so it is a trinomial.
3. SOLUTION: A polynomial is a monomial or the sum or difference of monomials. A monomial cannot have a variable in the
denominator of the fraction, so the term is not a monomial. Therefore, the expression is not a polynomial.
−3
4. ax
SOLUTION: There is only one term, however, there is a negative exponent, which means that there is a variable in the
denominator, so it is not a polynomial.
5. 3b
2
SOLUTION: A polynomial is a monomial or the sum or difference of monomials, so the expression is a polynomial. The
expression has only one term, so it is a monomial.
6. 2x
−3
− 4x + 1
SOLUTION: A polynomial is a monomial or the sum or difference of monomials. A monomial cannot have a variable in the
denominator. The first term can be represented as monomial. Therefore, the expression is not a polynomial.
, which is a fraction. So the first term is not a
7. POPULATION The table shows the population density for Nevada for various years.
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a. The population density d of Nevada from 1930 to 2000 can be modeled by d = 0.005y 2 − 0.127y + 1, where y
2
A polynomial is a monomial or the sum or difference of monomials. A monomial cannot have a variable in the
denominator. The first term can be represented as monomial.Quiz
Therefore, the expression is not a polynomial.
Mid-Chapter
, which is a fraction. So the first term is not a
7. POPULATION The table shows the population density for Nevada for various years.
a. The population density d of Nevada from 1930 to 2000 can be modeled by d = 0.005y 2 − 0.127y + 1, where y
2
represents the number of years since 1930. Identify the type of polynomial for 0.005y − 0.127y + 1.
b. What is the degree of the polynomial?
c. Predict the population density of Nevada for 2020. Explain your method.
SOLUTION: a. There are three terms in this expression, so it is a trinomial.
b. Find the degree of each term.
2
0.005y : degree 2
−0.127y: degree 1
1: degree 0
The degree of the polynomial is the highest degree of the terms, so it is 2.
c. Because 2020 is 90 years after 1930, let t be 90.
Find each sum or difference.
2
2
8. (y + 2y + 3) + (y + 3y – 1)
SOLUTION: 3
2
9. (3n – 2n + 7) – (n – 2n + 8)
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SOLUTION: Page 2
Mid-Chapter Quiz
3
2
9. (3n – 2n + 7) – (n – 2n + 8)
SOLUTION: 2
2
10. (5d + d ) – (4 – 4d )
SOLUTION: 2
11. (x + 4) + (3x + 2x – 7)
SOLUTION: 12. (3a – 3b + 2) – (4a + 5b)
SOLUTION: 2
2
13. (8x – y + 3) + (9 – 3x + 2y )
SOLUTION: Find each product.
2
14. 6y(y + 3y + 1)
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Mid-Chapter Quiz
Find each product.
2
14. 6y(y + 3y + 1)
SOLUTION: 2
15. 3n(n – 5n + 2)
SOLUTION: 2
2
16. d (–4 – 3d + 2d )
SOLUTION: 2
2
17. –2xy(3x + 2xy – 4y )
SOLUTION: 2
18. ab (12a + 5b – ab)
SOLUTION: 2 4
2
2
19. x y (3xy – x + 2y )
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MULTIPLE CHOICE Page 4
2
Mid-Chapter Quiz
2 4
2
2
19. x y (3xy – x + 2y )
SOLUTION: 2
20. MULTIPLE CHOICE Simplify x(4x + 5) + 3(2x – 4x + 1).
2
A 10x + 17x + 3
B 10x2 – 7x + 3
2
C 2x – 7x + 3
D 2x2 + 17x + 3
SOLUTION: Find each product.
21. (x + 2)(x + 5)
SOLUTION: 22. (3b – 2)(b – 4)
SOLUTION: 23. (n – 5)(n + 3)
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24. (4c – 2)(c + 2)
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Mid-Chapter Quiz
23. (n – 5)(n + 3)
SOLUTION: 24. (4c – 2)(c + 2)
SOLUTION: 2
25. (k – 1)(k – 3k )
SOLUTION: 2
26. (8d – 3)(2d + d + 1)
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