Find a polynomial function with following characteristics.
Degree: 4
Zero: 4 , multiplicity: 2
Zero: $- 3$, multiplicity: 2
Falls to the left,
Falls to the right
Absolute value of the leading coefficient is one
A) $y = x ^ { 4 } + x ^ { 3 } - 23 x ^ { 2 } + 24 x - 12$
B) $y = - x ^ { 4 } + x ^ { 3 } - 48 x ^ { 2 } + 9$
C) $y = x ^ { 4 } - 6 x ^ { 3 } - 18 x ^ { 2 } + 25 x + 48$
D) $y = - x ^ { 4 } + 2 x ^ { 3 } + 23 x ^ { 2 } - 24 x - 144$
E) $y = - x ^ { 4 } + 2 x ^ { 3 } - 24 x - 36$

Question

Quizplus · Accepted Answer

The correct polynomial must have a degree of 4, zeros at 4 (with multiplicity 2) and -3 (with multiplicity 2), and the leading coefficient must indicate it falls to the left and rises to the right. The leading coefficient's sign determines the end behavior: a positive leading coefficient means it rises to the right and falls to the left, and a negative leading coefficient means it falls to the right and rises to the left. Given the requirements, the polynomial must have a negative leading coefficient to fall to the left and rise to the right. Option D, $y = - x ^ { 4 } + 2 x ^ { 3 } + 23 x ^ { 2 } - 24 x - 144$, is the only one that meets all these criteria, including the correct end behavior and degree.

Find a Polynomial Function with Following Characteristics −3- 3−3 , Multiplicity: 2 Falls to the Left, Falls to the 4

Find a Polynomial Function with Following Characteristics $- 3$ , Multiplicity: 2
Falls to the Left,
Falls to the 4