SOLUTION: Hi There! Can You Please Help Me Solve This?? I Just Don't Know How To Take The First Step... Solve each equation over the complex numbers: x^3+5x^2+4x+20=0 Thank You So M

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Question 964570: Hi There! Can You Please Help Me Solve This?? I Just Don't Know How To Take The First Step...
Solve each equation over the complex numbers:
x^3+5x^2+4x+20=0
Thank You So Much!
Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website!
Rational Roots Theorem and synthetic division. The roots to check would be -1, -2, -4,- 5, -10, maybe -20.

You asked for a first step. Take as example 5; is one of the binomial factors of the cubic polynomial? Check the root -5 using synthetic division.

__________-5_______|_________1______5_______4_______20
__________________|
__________________|_______________-5________0______-20
___________________________________________________________
____________________________1______0______4_________0

Remainder is 0, so this means -5 is a root, or equivalently, (x+5) is one of the binomial factors of the polynomial given.

The quotient from the synthetic division shows the other factor is . This will have two complex roots.