SOLUTION: factor and solve f(x) =x^3+5x^2+9x+45

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: factor and solve f(x) =x^3+5x^2+9x+45      Log On


   

Question 131644: factor and solve
f(x) =x^3+5x^2+9x+45
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3%2B5x%5E2%2B9x%2B45 Start with the given equation

0=x%5E3%2B5x%5E2%2B9x%2B45 Plug in f(x)=0

0=%28x%5E3%2B5x%5E2%29%2B%289x%2B45%29 Group like terms


0=x%5E2%28x%2B5%29%2B9%28x%2B5%29 Factor out the GCF x%5E2 out of the first group. Factor out the GCF 9 out of the second group


0=%28x%5E2%2B9%29%28x%2B5%29 Since we have the common term x%2B5, we can combine like terms


x%5E2%2B9=0 or x%2B5=0 Set each factor equal to zero

x%5E2=-9 or x=-5 Isolate x for each case


x=0%2B-sqrt%28-9%29 or x=-5 Take the square root of both sides for the first case


x=3i, x=-3i or x=-5 Simplify



---------------------------
Answer:

So our solutions are

x=3i, x=-3i or x=-5