For each polynomial function, state the zeros and the multiplicity.
(1) f(x) = 4(x + 4) [(x + 3)]^2
(2) f(x) = 4x(x^2 - 3)
Ok, but I would like you to show me how you do the second one then
$\displaystyle f(x)=4(x+4)(x+3)^2$
You can see that $\displaystyle (x+4)$ divides f(x). More exactly, if x=-4, you can see that x+4=0, that is to say f(-4)=0. Thus -4 is a zero.
What for x+3 ? If x=-3, x+3=0. Then f(-3)=0. -3 is a zero.
Now, what are their multiplicity ?
The factor x+3 appears twice since it is $\displaystyle (x+3)^2=(x+3)(x+3)$. Its multiplicity is 2.A zero has a "multiplicity", which refers to the number of times that its associated factor appears in the polynomial.
The factor (x+4) appears only once. Its multiplicity is 1.