Question

4. What are the zeros of the function? What are their multiplicities?
F(x)=3x^3+15x^2+18x

Answer 1

factor a \(3x\) out first

Answer 2

I'll help you find the zeros

(this function is simpler than other cubic functions)

\[F(x)=3x^3+15x^2+18x~~~~~~~~~~~~~~~~~~set~~i t~~=0\]
\[0=3x^3+15x^2+18x~~~~~~~~~~~~~~~~~~~~factor~~out~~of~~x\]
\[0=(3x^2+15x+18)x\]
so one of the zeros is x=0
\[0=(3x^2+15x+18)~~~~⇒~~~3(x^2+5x+6)=0~~~~⇒~~~x^2+5x+6=0\]

Answer 3

\[(x+3)(x+2)=0~~~~So~~~~~x=-2~~~and~~~x=-3\]so you zeros are

\(\huge\color{magenta }{\huge {\bbox[5pt,yellow,border:2px solid red]{0,~~~-2,~~~-3}}}\)

Answer 4

Thanks