SOLUTION: Find the rational zeros and then the other zeros of the polynomial function f(x)=x^3-7x+6;that is,solve f(x)=0. Factor f(x) into linear factors.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the rational zeros and then the other zeros of the polynomial function f(x)=x^3-7x+6;that is,solve f(x)=0. Factor f(x) into linear factors.      Log On


   

Question 763532: Find the rational zeros and then the other zeros of the polynomial function f(x)=x^3-7x+6;that is,solve f(x)=0.
Factor f(x) into linear factors.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E3-7x%2B6
0=x%5E3-7x%2B6.......add 3x%5E2-3x%5E2 and write -7x as -9x%2B2x
0=x%5E3%2B3x%5E2-3x%5E2-9x%2B2x%2B6...group
0=%28x%5E3%2B3x%5E2%29-%283x%5E2%2B9x%29%2B%282x%2B6%29
0=x%5E2%28x%2B3%29-3x%28x%2B3%29%2B2%28x%2B3%29
0=%28x%2B3%29%28x%5E2-3x%2B2%29
0=%28x%5E2-3x%2B2%29%28x%2B3%29.... -3x as -x-2x
0=%28x%5E2-x-2x%2B2%29%28x%2B3%29..group
0=%28%28x%5E2-x%29-%282x-2%29%29%28x%2B3%29
0=%28x%28x-1%29-2%28x-1%29%29%28x%2B3%29
0=%28x-2%29%28x-1%29%28x%2B3%29
so, zeros are:
if 0=x-2 => x=2
if 0=x-1 => x=1
if 0=x%2B3 => x=-3

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+15%2C%28x-2%29%28x-1%29%28x%2B3%29%29+