Answer:
Part I: The degree of a polynomial is the greatest of the degrees of its terms.
Part II: In order to write a polynomial in descending order, you must write the terms with the exponents decreasing from left to right.
Part III: A. -4x² + 11x - 12, degree = 2,
B. 5x³ + 4x + 14, degree = 3.
Step-by-step explanation:
Part I : Since, the degree of a polynomial is the highest power of its monomials ( single term ),
eg : degree of
is 5.
Thus, in part I, the correct option is 'greatest'
Part II : When we write a polynomial then we write the terms of the polynomial in descending order of their degrees.
Thus, in part II the correct option is 'least'
Part III : A. ![-4x^2 - 12 + 11x](https://tex.z-dn.net/?f=-4x%5E2%20-%2012%20%2B%2011x)
∵ -4x² has the highest power in the polynomial.
⇒ Degree = 2,
Also, in the polynomial descending order of degrees,
2 > 1 > 0
⇒ polynomial in descending order,
![-4x^2 + 11x - 12](https://tex.z-dn.net/?f=-4x%5E2%20%2B%2011x%20-%2012)
B. ![2x^3 + 14 - 3x + 7x + 3x^3](https://tex.z-dn.net/?f=2x%5E3%20%2B%2014%20-%203x%20%2B%207x%20%2B%203x%5E3)
Combining like terms,
![5x^3 + 14+4x](https://tex.z-dn.net/?f=5x%5E3%20%2B%2014%2B4x)
∵ 5x³ has the highest degree,
⇒ Degree = 3,
Also, the order of the degrees in the polynomial is,
3 < 2 < 1 < 0
Thus, the polynomial in descending order,
![5x^3+4x + 14](https://tex.z-dn.net/?f=5x%5E3%2B4x%20%2B%2014)