f(x) = x^5 + 5x^4 + 20x^3 - 96x - 80 has some of its zeros as x = -2,-1, 2.  What would be the factorization of f(x)?  a) (x+2)(x+1)(x-2)(x+2-8i)(x+2+8i) b) (x+2)(x+1)(x-2)(x-2-8i)(x-2+8i)...

f(x) = x^5 + 5x^4 + 20x^3 - 96x - 80 has some of its zeros as x = -2,-1, 2.  What would be the factorization of f(x)? 

a) (x+2)(x+1)(x-2)(x+2-8i)(x+2+8i)

b) (x+2)(x+1)(x-2)(x-2-8i)(x-2+8i)

c) (x+2)(x+1)(x-2)(x+2-4i)(x+2+4i)

d) (x+2)(x+1)(x-2)(x-2-4i)(x-2+4i)

e) (x-2)(x-1)(x+2)(x+2-4i)(x+2+4i)

f) (x-2)(x-1)(x+2)(x-2-4i)(x-2+4i)

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

`f(x)=x^5+5x^4+20x^3-96x-80`

`=x^5+2x^4+3x^4+6x^3+14x^3+28x^2-28x^2-56x-40x-80`

`=(x+2)(x^4+3x^3+14x^2-28x-40)`

`=(x+2)(x^4+x^3+2x^3+2x^2+12x^2+12x-40x-40)`

`=(x+2)(x+1)(x^3+2x^2+12x-40)`

`=(x+2)(x+1)(x^3-2x^2+4x^2-8x+20x-40)`

`=(x+2)(x+1)(x-2)(x^2+4x+20)`

`=(x+2)(x+1)(x-2)(x+2-4i)(x+2+4i)`

Correct choice is (c).

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