SOLUTION: Factor the polynomial f(x)=x^3+3x^2-2x-6 into linear factors using two methods: Grouping method and rational zeros'

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the polynomial f(x)=x^3+3x^2-2x-6 into linear factors using two methods: Grouping method and rational zeros'      Log On


   

Question 1130201: Factor the polynomial f(x)=x^3+3x^2-2x-6 into linear factors using two methods: Grouping method and rational zeros'
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Grouping method and rational zeros'
Grouping method:
f%28x%29=x%5E3%2B3x%5E2-2x-6+
f%28x%29=%28x%5E3%2B3x%5E2%29-%282x%2B6+%29
f%28x%29=x%5E2%28x%2B3%29-2%28x%2B3+%29
f%28x%29=%28x%5E2-2%29%28x%2B3+%29
f%28x%29=%28x%5E2-%28sqrt%282%29%29%5E2%29%28x%2B3+%29
f%28x%29=%28x-sqrt%282%29%29%28x%2Bsqrt%282%29%29%28x%2B3+%29

rational zeros' method: square both sides
0=sqrt%28x%5E3%2B3x%5E2-2x-6%29+
0=sqrt%28%28x+%2B+3%29+%28x%5E2+-+2%29%29
0=sqrt%28x+%2B+3%29+sqrt%28x%5E2+-+2%29
roots:
if 0=sqrt%28x+%2B+3%29+->x%2B3=0->x=-3
if 0=+sqrt%28x%5E2+-+2%29->x%5E2+-+2=0->x%5E2+=+2->x+=+sqrt%282%29 or x+=+-sqrt%282%29