Problema Solution
Solve the following equation in the real number system. Please show all of your work.
x^3+7x^2+14+8=0
Answer provided by our tutors
x^3 + 7x^2 + 14x + 8 = 0
=> x^3 + 4x^2 + 3x^2 + 12x + 2x + 8 = 0
=> x^2(x +4) + 3x(x +4) + 2(x+4) = 0
=> (x+4)(x^2 + 3x + 2) = 0
=> (x+4)(x^2 + x + 2x + 2) = 0
=> (x+4)[x(x+1) + 2(x+1)] = 0
=> (x+4)(x+1)(x+2) = 0
=> x=-4 or x=-1 or x=-2