Find all zeros of the function and write the polynomial as a product of linear factors.

f(x)=x^4+6x^3+12x^2+24x+32
a.) f(x)=(x-1)(x-8)(x-2i)(x+2i)
b.) f(x)=(x-i√8)(x+i√8)(x-2)(x+2)
c.) f(x)=(x-2)(x+4)(x-2)(x+2)
d.) f(x)=(x+2)(x+4)(x-2i)(x+2i)

Please, show all works.

Question

Find all zeros of the function and write the polynomial as a product of linear factors.

f(x)=x^4+6x^3+12x^2+24x+32
a.) f(x)=(x-1)(x-8)(x-2i)(x+2i)
b.) f(x)=(x-i√8)(x+i√8)(x-2)(x+2)
c.) f(x)=(x-2)(x+4)(x-2)(x+2)
d.) f(x)=(x+2)(x+4)(x-2i)(x+2i)

Please, show all works.

loser66 · Answer

if you plug 1 into f(x) , do you get 0 ?

anonymous · Answer

no.

loser66 · Answer

so, get rid of the first option, right?

loser66 · Answer

try the second one, pick the easiest case, x = 2 from (x-2) =0, is f(2) =0?

anonymous · Answer

but it all positive so it can't equal to 0.

loser66 · Answer

if you can see it, very good, safe time, just have the last one which have negative value, try.

loser66 · Answer

f(-2) = 0??
f(-4) =0 ??

anonymous · Answer

f(-2) is equal to 0.

loser66 · Answer

good,

anonymous · Answer

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