Describing Polynomials practice worksheet with exercises on degree, standard form, classification, and end behavior.

1. An odd-degree polynomial must have at least one real root.
2. A polynomial function is written in standard form if terms are written in descending order of exponents from left to right.
3. The leading coefficient is the number in front of the term with the highest exponent in the polynomial.
4. A monomial has one term, a binomial has two terms, and a trinomial has three terms.
5. It is possible for an even-degree polynomial to have no real zeros.
6. The degree of a polynomial function is used to determine the end behavior of the graph of a polynomial function.

7. y = -x² - 2x
Standard Form: y = -x² - 2x
Degree: 2
Classify by degree: Quadratic
Classify by number of terms: Binomial
LC: -1
End Behavior: ↓↑

8. y = 3x³ + x² - (-x⁴/2)
Standard Form: y = (1/2)x⁴ + 3x³ + x²
Degree: 4
Classify by degree: Quartic
Classify by number of terms: Trinomial
LC: 1/2
End Behavior: ↑↑

9. y = (2x)³ + 3x - 1
Standard Form: y = 8x³ + 3x - 1
Degree: 3
Classify by degree: Cubic
Classify by number of terms: Trinomial
LC: 8
End Behavior: ↓↑

10. y = (x + 2)³ + 3
Standard Form: y = x³ + 6x² + 12x + 11
Degree: 3
Classify by degree: Cubic
Classify by number of terms: Polynomial (4 terms)
LC: 1
End Behavior: ↓↑

11. y = (2 + x)(2 - x) - 4
Standard Form: y = -x²
Degree: 2
Classify by degree: Quadratic
Classify by number of terms: Monomial
LC: -1
End Behavior: ↓↓

12. y = 3(x + 1)² - 3x²
Standard Form: y = 6x + 3
Degree: 1
Classify by degree: Linear
Classify by number of terms: Binomial
LC: 6
End Behavior: ↓↑

13. y = 2x - 2(2x - 3)
Standard Form: y = -2x + 6
Degree: 1
Classify by degree: Linear
Classify by number of terms: Binomial
LC: -2
End Behavior: ↑↓