EXPLANATION
Given the function:
[tex]-3x^3-15x^2+12x+60[/tex]
Factor out common term -3:
-3(x^3 -5x^2 -4x -20)
Factor x^3 -5x^2-4x-20:
[tex]=(x^3-5x^2)+(-4x-20)[/tex]
Factor out -4 from -4x - 20:
-4x - 20
Rewrite 20 as 4*5:
=-4x - 4*5
Factor out common term -4:
=-4(x+5)
Factor out x^2 from x^3 + 5x^2:
Apply exponent rule: a^(b+c)= a^b*a^c
x^3=xx^2
=xx^2 + 5x^2
Factor out common term x^2:
=x^2(x+5)
=-4(x+5) + x^2(x+5)
Factor out common term x+5
=(x+5)(x^2-4)
Factor x^2-4:
Rewrite 4 as 2^2:
=x^2-2^2
Apply difference of two squares formula:
[tex]x^2-2^2=(x+2)(x-2)[/tex]
The resultant expression is:
[tex]=3(x+5)(x+2)(x-2)[/tex]
So, the zeros are:
(-5,0) (-2,0) (2,0)
