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