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

Question

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

anonymous · Answer

factor a $3x$ out first

solomonzelman · Answer

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
$$0=(3x^2+15x+18)~~~~⇒~~~3(x^2+5x+6)=0~~~~⇒~~~x^2+5x+6=0$$

solomonzelman · Answer

$$(x+3)(x+2)=0~~~~So~~~~~x=-2~~~and~~~x=-3$$so you zeros are

$\huge\color{magenta }{\huge {\bbox[5pt,yellow,border:2px solid red]{0,~~~-2,~~~-3}}}$

anonymous · Answer

Thanks