SOLUTION: Tutors Find only the rational zeros of the function f(x)=2x^3+3x^2+2x+3 Thanx a Bunch!

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Question 145262: Tutors
Find only the rational zeros of the function
f(x)=2x^3+3x^2+2x+3
Thanx a Bunch!
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
factor by grouping:
0=2x^3+3x^2+2x+3
0=2x(x^2+1)+3(x^2+1)
0=(2x+3)(x^2+1)
So 0=2x+3 or x^2+1=0
This can only be when 0=-3/2 (the x^2+1 is always>0 thus the solutions must be imaginary).
check via graph:
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E3%2B3x%5E2%2B2x%2B3++%29