8-1 Adding and Subtracting Polynomials
Determine whether each expression is a
polynomial. If it is a polynomial, find the degree
and determine whether it is a monomial,
binomial, or trinomial.
20. SOLUTION: A monomial is a number, a variable, or the product of
a number and one or more variables with
nonnegative integer exponents. It has
is a division of two monomials, so
only one term. it is not a monomial.
4
2
22. c – 2c + 1
SOLUTION: A polynomial is a monomial or the sum of
4
2
monomials. c – 2c + 1 is the sum of 3 monomials,
so it is a polynomial. The degree of a polynomial is the greatest degree of
any term in the polynomial. The degree of each term
4
2
is 4, 2, and 0, so the degree of c – 2c + 1 is 4. The
polynomial has three terms, so it is a trinomial.
24. a – a
2
SOLUTION: A polynomial is a monomial or the sum of
2
monomials. a – a is the sum of 2 monomials, so it is
a polynomial. The degree of a polynomial is the greatest degree of
any term in the polynomial. The degree of each term
is 1 and 2, so the degree of a – a2 is 2. The
polynomial has two terms, so it is a binomial.
Write each polynomial in standard form. Identify
the leading coefficient.
2
26. 5x – 2 + 3x
SOLUTION: Find the degree of each term.
2
5x → 2
– 2 → 0
3x → 1
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2
The greatest degree is 2, from the term 5x , so the
2
The degree of a polynomial is the greatest degree of
any term in the polynomial. The degree of each term
is 1 and 2, so the degree of a – a2 is 2. The
polynomial has two terms, so it is a binomial.
Write each polynomial in standard form. Identify
the leading coefficient.
2
26. 5x – 2 + 3x
SOLUTION: Find the degree of each term.
2
5x → 2
– 2 → 0
3x → 1
2
The greatest degree is 2, from the term 5x , so the
2
leading coefficient of 5x – 2 + 3x is 5.
Rewrite the polynomial with each monomial in
descending order according to degree.
2
5x + 3x – 2
28. 4 – 3c – 5c
2
SOLUTION: Find the degree of each term.
4 → 0
3c → 1
2
– 5c → 2
2
The greatest degree is 2, from the term – 5c , so the
2
leading coefficient of 4 – 3c – 5c is –5.
Rewrite the polynomial with each monomial in
descending order according to degree.
2
–5c – 3c + 4
2
5
30. 11t + 2t – 3 + t
SOLUTION: Find the degree of each term.
11t → 1
2
2t → 2
–3 → 0
t 5 → 5
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5
The greatest degree is 5, from the term t , so the
2
5
Rewrite the polynomial with each monomial in
descending order according to degree.
8-1 Adding
and Subtracting Polynomials
Rewrite the polynomial with each monomial in
descending order according to degree.
2
–5c – 3c + 4
2
5
Find each sum or difference.
2
34. (2c + 6c + 4) + (5c – 7)
30. 11t + 2t – 3 + t
SOLUTION: Find the degree of each term.
SOLUTION: 11t → 1
2
2t → 2
–3 → 0
t 5 → 5
3
2
36. (3c − c + 11) − (c + 2c + 8)
5
The greatest degree is 5, from the term t , so the
2
5
leading coefficient of 11t + 2t – 3 + t is 1.
SOLUTION: Rewrite the polynomial with each monomial in
descending order according to degree.
5
2
t + 2t + 11t – 3
32. 38. (2x − 2y + 1) − (3y + 4x)
SOLUTION: Find the degree of each term.
SOLUTION: → 0
–3x 4 → 4
7 → 0
2
2
2
40. (x y − 3x + y) + (3y − 2x y)
SOLUTION: 4
The greatest degree is 4, from the term –3x , so the
leading coefficient of
is –3.
Rewrite the polynomial with each monomial in
descending order according to degree.
2
2
42. (5n − 2p + 2np) − (4p + 4n)
SOLUTION: Find each sum or difference.
2
34. (2c + 6c + 4) + (5c – 7)
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3
2
36. (3c − c + 11) − (c + 2c + 8)
Classify each polynomial according to its degree
and number of terms.
3
46. 11z
Page 2
SOLUTION: Find the degree of each term.
6t → 3
The greatest degree is 3 and there are 3 terms, so
2
3
10t – 4t + 6t is a cubic trinomial.
8-1 Adding and Subtracting Polynomials
Classify each polynomial according to its degree
and number of terms.
3
46. 11z
61. CCSS CRITIQUE Cheyenne and Sebastian are
2
2
finding (2x − x) − (3x + 3x − 2). Is either of them
correct? Explain your reasoning.
SOLUTION: Find the degree of each term.
11z 3 → 3
The greatest degree is 3 and there is one term, so
11z 3 is a cubic monomial.
3
48. 3x – 7
SOLUTION: 3
Find the degree of each term of 3x – 7.
SOLUTION: 3
3x → 3
–7 → 0
The greatest degree is 3 and there are 2 terms, so
3
3x – 7 is a cubic binomial.
2
3
50. 10t – 4t + 6t
SOLUTION: 2
3
Find the degree of each term of 10t – 4t + 6t .
10t → 1
2
4t → 2
Neither is correct. Cheyenne, did not distribute the
negative to the 2nd and 3rd terms when she found
the additive inverse. Sebastian did not distribute the
negate to the 3rd terms when he found the additive
inverse. To find the additive inverse, all terms should
be multiplied by −1.
66. Three consecutive integers can be represented by x,
x + 1, and x + 2. What is the sum of these three
integers?
3
6t → 3
A x(x + 1)(x + 2)
The greatest degree is 3 and there are 3 terms, so
2
3
10t – 4t + 6t is a cubic trinomial.
61. CCSS CRITIQUE Cheyenne and Sebastian are
2
2
finding (2x − x) − (3x + 3x − 2). Is either of them
correct? Explain your reasoning.
B x3 + 3
C 3x + 3
D x + 3
SOLUTION: The correct choice is C.
69. Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
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D x + 3
SOLUTION: 8-1 Adding and Subtracting Polynomials
The correct choice is C.
69. Which ordered pair is in the solution set of the
system of inequalities shown in the graph?
A (−3, 0)
B (0, −3)
C (5, 0)
D (0, 5)
SOLUTION: Choice A is outside the shaded area for both
inequalities. Choices B and D are inside the shaded
area for only one inequality. Choice C is the only
point in the solution for both inequalities. So, the correct choice is C.
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