What is the intuition to factoring a problem like 2x^4+3x^3-5x^2+3x+2. or just finding the 0s

Find the gradient of f(x,y,z)equals=left parenthesis x squared plus y squared plus z squared right parenthesis superscript negative 1 divided by 2 baseline plus ln left parenthesis x right parenthesis x2+y2+z2−1/2+ln(xyz) at the point left parenthesis negative 2 comma 1 comma negative 2 right parenthesis(−2,1,−2).

Me! 50 points! why does when we come home, our door is unlocked and there is grease on the door knob, me solve this , and i don't know what category this goes under

Solve the equation w^3 = 1,000 i honestly dont know how to punch this into a calculator pls