Answer:
[tex]\boxed{\sf \ \ \ -2(x+2)(x-3)^3 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
We are looking for a polynomial of lowest degree with zeros of -2 (multiplicity 1), 3 (multiplicity 3),
so it comes [tex]k(x-(-2))^1(x-3)^3=k(x+2)(x-3)^3[/tex]
where k is real and then we need to translate the following "with f(0) = 108."
to find k
[tex]k(0+2)(0-3)^3=108\\<=>k*2*(-1)^3*3^3=108\\<=>-54*k=108\\<=> k=\dfrac{108}{54}=-2[/tex]
so the answer is
[tex]-2(x+2)(x-3)^3[/tex]
hope this helps
