Answer:
P(x) = 0.4*(x-1)(x-1)(x)(x+1)
Step-by-step explanation:
P(x) is a polynomial of degree 4, so it has 4 roots. The roots of P(x) are:
1, 1, 0, -1.
A general form for a polynomial of degree 4 is:
P(x) = a(x-x1)(x-x2)(x-x3)(x-x4)
where 'a' is a constant coefficient, and x1, x2, x3 and x4 are the roots.
So, we have that:
P(x) = a(x-1)(x-1)(x)(x+1)
We know that the polynomial goes through the point (5,192), so using the value of x=5, we have that P(x)=192. Using these values, we can find the value of 'a':
192 = a(5-1)(5-1)(5)(5+1)
192 = a*4*4*5*6
480*a = 192
a = 192/480 = 0.4
So we have that P(x) = 0.4*(x-1)(x-1)(x)(x+1)
