SOLUTION: Find the complex zeros of each polynomial function. write f in factored form. f(x)=x^4+ 2x^3 + 22x^2 +50x- 75

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the complex zeros of each polynomial function. write f in factored form. f(x)=x^4+ 2x^3 + 22x^2 +50x- 75      Log On


   

Question 733134: Find the complex zeros of each polynomial function. write f in factored form.
f(x)=x^4+ 2x^3 + 22x^2 +50x- 75
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
x^4+ 2x^3 + 22x^2 +50x- 75=
(2x^3 +50x)+(x^4 + 22x^2 - 75)=
2x(x^2 +25)+(x^4 + 25x^2 -3x^2- 75)=
2x(x^2 +25)+(x^4 + 25x^2) -(3x^2+ 75)=
2x(x^2 +25)+x^2(x^2 + 25) -3(x^2+ 25)=
(x^2 +25)(x^2+2x-3)=
(x^2+25)(x+3)(x-1)

zeros: {-5i, 5i, -3, 1}



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