Find a polynomial function with following characteristics.
Degree: 4
Zero: $ -1 $, multiplicity: 2
Zero: $ -3 $, multiplicity: 2
Falls to the left,
Falls to the right
Absolute value of the leading coefficient is one

A) $y = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } + 24 x + 3$
B) $y = - x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 9$
C) $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 10 x + 3$
D) $y = - x ^ { 4 } - 8 x ^ { 3 } - 22 x ^ { 2 } - 24 x - 9$
E) $y = - x ^ { 4 } - 8 x ^ { 3 } - 24 x + 9$

Question

Find a polynomial function with following characteristics.
Degree: 4
Zero: $ -1 $, multiplicity: 2
Zero: $ -3 $, multiplicity: 2
Falls to the left,
Falls to the right
Absolute value of the leading coefficient is one

A) $y = x ^ { 4 } - 4 x ^ { 3 } + 22 x ^ { 2 } + 24 x + 3$
B) $y = - x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 9$
C) $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 10 x + 3$
D) $y = - x ^ { 4 } - 8 x ^ { 3 } - 22 x ^ { 2 } - 24 x - 9$
E) $y = - x ^ { 4 } - 8 x ^ { 3 } - 24 x + 9$

Quizplus · Accepted Answer

The polynomial must have a degree of 4 with zeros at -1 and -3, each with multiplicity 2, and the leading coefficient must be negative for the function to fall to both the left and right. Option D satisfies all these conditions.

Find a Polynomial Function with Following Characteristics −1 -1 −1 , Multiplicity: 2 Zero

Find a Polynomial Function with Following Characteristics $-1$ , Multiplicity: 2
Zero