Define Me!
Polynomial Vocabulary
Compare and contrast the examples and counterexamples write a definition for each term on your answer sheet.
Compare definitions with your group. [Please do not write on this document.]
Polynomial
Examples:
Counterexamples:
1. 2x  3x  4
2. 5xy
1. x 3  3x  1
2
2. x
3.  8x 7  2x 5  3x  1
4.  x 3  1.5x 4  6
3.
5x 3
 3x 8  7
4
4.
5.
2
3
5
x3 5
x
x  x 2 3x 2.6
Standard form
Examples:
Counterexamples:
1. 3x  5x  4
1. x  3x 2  1
2. 5x 7  3x 5  x  5
2. 10  x 3  2x 4
4. 1.5x 4  6x 2  20x
3. 5  x 3  5x 6  2x
2
Degree of a term
Examples:
Counterexamples:
2. x  3x  2x  5
7
2. x 7  3x 3  2x  5
3
7 is the degree of the first term
3 is the degree of the second term
1 is the degree of the third term
0 is the degree of the fourth term
1 is not the degree of the first term
3 is not the degree of the second term
-2 is not the degree of the third term
5 is not the degree of the fourth term
Degree of a polynomial
Examples:
Counterexamples:
1. 3x  5x  4
1. 3x 2  5x  4
2
2 is the degree of the polynomial
2.  4x  3x  x  5
2
5
3 is not the degree of the polynomial
2.  4x 2  3x 5  x  5
5 is the degree of the polynomial
4. 1  x  x  x  x
2
5. 10x
3
4
4 is the degree of the polynomial
1 is the degree of the polynomial
2 is not the degree of the polynomial
4. 1  x 2  x 3  x  x 4
5. 10x
-1 is not the degree of the polynomial
10 is not the degree of the polynomial
Leading coefficient
Examples:
Counterexamples:
1. 3x  5x  4
1. 3x 2  5x  4
2
3 is the leading coefficient
2. 9x  5x  4x
2
3
5 is the leading coefficient
3. 10  5x  4x  x
3
6
-4 is the leading coefficient
Monomial
2 is not the leading coefficient
2. 9x  5x 3  4x
2
9 is not the leading coefficient
3. 10  5x 3  4x 6  x
6 is not the leading coefficient
Examples:
Counterexamples:
Binomial
Examples:
Counterexamples:
1. 3x  5x
1. 3x 2
2.  5x 7  3x 5
2.  5x 7  3x 5  5
3. x  x 5
3. x  x 5  x 3  2
2
Trinomial
Examples:
Counterexamples:
1. 3x  5x  4
2. 5x  3x 5  5
1. 3x 2  5x
2. 5x
3. x 7  x 5  x
3. 3x 7  x  2  x 3
2
Constant
Examples:
Counterexamples:
1.  4
2. 1.6
4.
5.  64839
1. 3x
2.  x 3  2x 4
3.  5x 6
4. x
Linear
Examples:
2.  x  5
1. 5x  4
3. x
4.
6x
Counterexamples:
1. 5x  3x 2  4
2. x 3
3. 5  x 3
4. 3x  2x 2
5. 2x 2
1
5. 8  x
2
Quadratic
Examples:
Counterexamples:
1. 3x  5x  4
2. 5x
3. x  x 2
4.  1.5x 2  20
2
2
1. x  1
2. 10  x 2  2x 4
3. 5x 2  x 3
4.  7  3x
Cubic
Examples:
Counterexamples:
1.  8x  3x  5x  4
1.  8x 4  3x 3  5x  4
2. 5x 2  3x 3
2.  x 3  2x 4
3. 10  x 3  x
3. 5  x 3  5x 6
3
2
Quartic
Examples:
Counterexamples:
1. 3x  5x  4
1. 3x 3  5x  4
2. 5x 3  3x 4  x  5
2. 5x 3  3x 2  x  5
4. 1.5x 4
4. 1.5x 2
4