Question

Which of the following must be true about p?

A. p(x) has an even degree.
B. p(x) has an odd degree.
C .p(x) has a positive leading coefficient.
D. p(x) has a negative leading coefficient.
E. p(x) has a positive constant term.
F. p(x) has a negative constant term.
G. In p(x), the zero 1 has an even multiplicity.
H. In p(x), the zero 1 has an odd multiplicity.

Answer 1

9514 1404 393

Answer:

B, C, F, H

Explanation:

When the function has end behavior that goes to opposite infinities, the degree must be odd, as here.

When the function goes to infinity with the same sign as the variable, then the leading coefficient must be positive, as here.

When the function crosses the y-axis at a negative value, the constant must be negative, as here.

When the function crosses the x-axis at a zero, the zero must have odd multiplicity, as for the zero x=1 here.

Choices B, C, F, H apply.