SOLUTION: f(x)=x^3+3x^2-5x^+8 x=4 Could you please help with this problem. The question is to decide whether the x value of 4 is a zero of the function. We can't figure out how to factor the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: f(x)=x^3+3x^2-5x^+8 x=4 Could you please help with this problem. The question is to decide whether the x value of 4 is a zero of the function. We can't figure out how to factor the      Log On


   

Question 123865This question is from textbook McDougal Littell Algebra 2
: f(x)=x^3+3x^2-5x^+8 x=4 Could you please help with this problem. The question is to decide whether the x value of 4 is a zero of the function. We can't figure out how to factor the polynomial. This question is from textbook McDougal Littell Algebra 2

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You don't need to factor the polynomial to determine if a particular value is a zero. All you need to do is evaluate f%284%29.

If f%28x%29=x%5E3%2B3x%5E2-5x%2B8 then f%284%29=%284%29%5E3%2B3%284%29%5E2-5%284%29%2B8

f%284%29=64%2B48-20%2B8%3C%3E0, so no, 4 is not a zero of the polynomial

graph%28600%2C600%2C-10%2C10%2C-3%2C40%2Cx%5E3%2B3x%5E2-5x%2B8%29

Actually, this thing has one real zero somewhere near -4.5 and a conjugate pair of complex zeros that would be more work to calculate than I would care to do. Google the general solution of the cubic if you are curious.