What is the polynomial function P(x) if leading term=4x^3, constant term=1, P(1)=9, P(-1)=-5

Is there 2 polynomial functions?

P(x) = 4x^3 + ax^2 + bx + 1
P(1) = 4 + a + b + 1 = 9
P(-1) = -4 + a -b + 1 = -5
Solving these 2 equations,
a = 1, b = 3
Thus
P(x) = 4x^3 + x + 3x + 1

P(x) = 4x³ + ax² + bx + 1

P(1) = 9
4(1) + a(1) + b(1) + 1 = 9 ---------> a + b = 4

P(−1) = −5
4(−1) + a(1) + b(−1) + 1 = −5 ----> a − b = −2

a + b = 4
a − b = −2
-------------
2a = 2
a = 1
b = 3

P(x) = 4x³ + x² + 3x + 1