Classifying Polynomials

Show your work for each problem.

1.
How many terms does have?
1. a)2
2. b)4
3. c)3
4. d)5
Answer: 3
The polynomial has three terms: , , and . This makes it a trinomial.
2.
What is the degree of ?
1. a)3
2. b)2
3. c)4
4. d)1
Answer: 1
The highest power of is 2 (in ), so the degree is 2. This is a quadratic polynomial.
3.
Which of the following is a monomial?
1. a)
2. b)
3. c)
4. d)
Answer:
is the only monomial because it has just one term. The others have 2 or 3 terms.
4.
A polynomial of degree 3 is called:
1. a)Quadratic
2. b)Cubic
3. c)Quartic
4. d)Linear
Answer: Cubic
A degree 3 polynomial is called cubic. Linear is degree 1, quadratic is degree 2, and quartic is degree 4.
5.
What type of polynomial is ?
1. a)Quadratic trinomial
2. b)Linear binomial
3. c)Quadratic binomial
4. d)Cubic trinomial
Answer: Quadratic trinomial
It has 3 terms (trinomial) and the highest exponent is 2 (quadratic). So it's a quadratic trinomial.
6.
What is the degree of the constant polynomial ?
Answer: 0
A constant like can be written as . The highest (and only) exponent is 0, so the degree is 0.
7.
How many terms does have?
Answer: 1
is a single term with no addition or subtraction. It's a monomial (1 term).
8.
What is the degree of ?
Answer: 5
The term has the highest power. The exponent is 5, so the degree is 5. This is a quintic polynomial.
9.
How many terms does have?
Answer: 4
There are 4 terms: , , , and . With 4 or more terms, we simply call it a polynomial.
10.
After simplifying , what is the degree?
Answer: 2
Simplify: , giving . The highest power is 2, so degree is 2.
11.
Classify completely.
Answer: linear binomial
1. How many terms does have? 2
2. What do we call a polynomial with 2 terms? binomial
3. What is the highest exponent? 1
4. What do we call a degree-1 polynomial? linear
12.
Write in standard form and classify it.
Answer: quadratic trinomial
1. What is the degree of each term? List them. 0, 2, 1
2. Which term should come first in standard form? -x^2
3. Write the polynomial in standard form. -x^2 + 3x + 4
4. What is the full classification? quadratic trinomial
13.
Classify completely.
Answer: quartic binomial
1. How many terms does have? 2
2. What is the highest exponent? 4
3. What do we call a degree-4 polynomial? quartic
4. What is the full classification? quartic binomial
14.
Simplify and classify .
Answer: cubic trinomial
1. Combine the terms: 3x^3
2. Combine the terms: -4x^2
3. Write the simplified polynomial. 3x^3 - 4x^2 + 5
4. What is the full classification? cubic trinomial
15.
Classify after simplifying.
Answer: quadratic binomial
1. What is ? 0
2. What polynomial remains? 2x^2 - 7
3. What is the degree of the simplified polynomial? 2
4. What is the full classification? quadratic binomial
16.
A polynomial has 3 terms and its highest term is . What is its degree?
Answer: 5
The highest term has exponent 5, so the degree is 5. This would be a quintic trinomial.
17.
Is a polynomial? Explain why or why not.
Answer: no
1. What is written with an exponent? 2x^-1
2. Is a non-negative integer? no
3. What exponents are allowed in polynomials? non-negative integers
4. Is this expression a polynomial? no