Answer:
The expression for f(x) is:
f(x) = (x+5)(x+5)(x+5)(x+4)(x-2)(x-9)
Step-by-step explanation:
We know that for any polynomial equation with roots:
[tex]a_1,a_2,a_3,...[/tex] with multiplicity:
[tex]m_1,m_2,...[/tex]
the equation for the polynomial is given by:
[tex]f(x)=(x-a_1)^{m_1}(x-a_2)^{m_2}......[/tex]
if the leading coefficient is negative we may take '-' sign in the starting of the expression.
Here we are given that :
f(x) has a leading coefficient of 1, roots –4, 2, and 9 with multiplicity 1, and root –5 with multiplicity 3
Hence, f(x) is given by:
[tex]f(x)=(x-(-4))^{1}(x-2)^{1}(x-9)^{1}(x-(-5))^{3}\\\\\\i.e.\\\\\\f(x)=(x+4)(x-2)(x-9)(x+5)^3\\\\\\f(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)[/tex]
Hence, the expression for f(x) is:
[tex]f(x)=(x+5)(x+5)(x+5)(x+4)(x-2)(x-9)[/tex]
