Question

12. Which of these is True concerning polynomials (Select All)

A) A degree 7 polynomial can have up to 7 extrema.
B) The degree of y = 7x4 - 6x² + 4x - 1 is 7.
C) A cubic must have at least 1 real root.
D) The degree of y = (x − 2)ª (x +4)³ (x + 3)² is 9.
E) A degree 5 polynomial can have up to 5 roots.​

Answer 1

A degree 7 polynomial can have up to 7 extrema, a cubic must have at least 1 real root, and a degree 5 polynomial can have up to 5 roots.

Step-by-step explanation:

The correct statements concerning polynomials are:

1. A) A degree 7 polynomial can have up to 7 extrema. This is true because the number of extrema is equal to the degree of the polynomial.
2. C) A cubic must have at least 1 real root. This is true because the Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n complex roots.
3. E) A degree 5 polynomial can have up to 5 roots. This is true because the number of roots is equal to the degree of the polynomial.

Answer 2

12. Which of these is True concerning polynomials (Select All)

A) A degree 7 polynomial can have up to 7 extrema.

B) The degree of y = 7x4 - 6x² + 4x - 1 is 7.

C) A cubic must have at least 1 real root.

D) The degree of y = (x − 2)ª (x +4)³ (x + 3)² is 9.

E) A degree 5 polynomial can have up to 5 roots.