Question

identify all rational zeros of the polynomial function f(x)=x^3+2x^2-3x+20

Answer 1

What are you studying? Factoring polynomials maybe? This would help guide me toward the method most suitable.

Answer 2

I'm going to solve this by factoring it. So since the last number is 20 and the coefficient of the highest power of x is 1, I can conclude the positive and negative factors of 20 are possible roots. I don't remember the name of that theorem but I remember having seen it. Regardless, it comes to trial and error. Pick some factors (I generally start with factors like 1,-1 if possible since they're easier) to try. I use synthetic division to see if they are factors because I like it best.

Answer 3

I found x+4 was a factor. This gives:\[x ^{3}+2x ^{2}-3x+20=(x+4)(x ^{2}-2x+5)\]
The second term does not factor into rational roots (they are imaginary). Therefore the only rational root is x=-4.