Introduction to Polynomials

Show your work for each problem.

1.
How many terms does the polynomial have?
1. a)5
2. b)4
3. c)3
4. d)2
Answer: 3
The polynomial has 3 terms: , , and . Count each part separated by + or - signs.
2.
What is the coefficient of in the polynomial ?
1. a)-2
2. b)-5
3. c)7
4. d)4
Answer: -2
The term with is , so the coefficient is . Remember to include the negative sign!
3.
What type of polynomial is ?
1. a)Binomial
2. b)Monomial
3. c)Polynomial with 4 terms
4. d)Trinomial
Answer: Monomial
has only one term, so it's a monomial. 'Mono' means one.
4.
What is the degree of the polynomial ?
Answer: 4
The exponents are 4, 2, 1, and 0. The highest is 4, so the degree is 4.
5.
What is the constant term in the polynomial ?
Answer: -8
The constant term is because it has no variable attached. Don't forget the negative sign!
6.
Which expression is NOT a polynomial?
1. a)
2. b)
3. c)
4. d)
Answer:
has a negative exponent, so it's NOT a polynomial. All others have valid exponents.
7.
What is the leading coefficient of ?
1. a)2
2. b)5
3. c)-1
4. d)-3
Answer: 2
The term with the highest degree is (degree 4). Its coefficient is .
8.
How many terms does the polynomial have?
Answer: 5
The 5 terms are: , , , , and .
9.
What is the coefficient of in the polynomial ? (Enter a number)
Answer: 0
There is no term in , which means its coefficient is 0. The polynomial is equivalent to .
10.
Write the polynomial in standard form.
Answer: 5x^3 - x^2 - 2x + 7
1. What is the highest degree term? 5x^3
2. What is the degree 2 term? -x^2
3. What is the degree 1 term? -2x
4. What is the constant term (degree 0)? 7
11.
Classify the polynomial by its degree and number of terms.
Answer: Quadratic trinomial
1. How many terms does this polynomial have? 3
2. What is the highest exponent? 2
3. What do we call a polynomial with 3 terms? trinomial
4. What do we call a polynomial of degree 2? quadratic
12.
For the polynomial , identify: (a) degree, (b) leading coefficient, (c) constant term, (d) number of terms.
Answer: 4, -2, 8, 4
1. What is the degree (highest exponent)? 4
2. What is the leading coefficient (coefficient of highest degree term)? -2
3. What is the constant term (no variable)? 8
4. How many terms are there? 4
13.
What is the degree of the term in a two-variable polynomial?
Answer: 5
The degree is . Add the exponent of (which is 3) and the exponent of (which is 2).
14.
Determine if is a polynomial. Explain why or why not.
Answer: Not a polynomial
1. What is written with an exponent? x^(1/2)
2. Is 1/2 a non-negative integer? no
3. What type of exponent do polynomials require? non-negative integer
4. Is this expression a polynomial? no
15.
Write a cubic binomial in standard form with a leading coefficient of -4.
Answer: -4x^3 + (any term)
1. What degree must a cubic polynomial have? 3
2. How many terms must a binomial have? 2
3. What is the leading term with coefficient -4? -4x^3
4. Write one possible answer (example: -4x^3 + 5) -4x^3 + 5
16.
For the polynomial , find the degree of each term and the degree of the polynomial.
Answer: 5, 3, 1, 0; degree 5
1. What is the degree of ? (Add exponents) 5
2. What is the degree of ? 3
3. What is the degree of ? 1
4. What is the degree of the polynomial? 5