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How can long division and synthetic division be used to find zeros of polynomial functions?

Question

Reallly need Help!!! Will give medal. 



How can long division and synthetic division be used to find zeros of polynomial functions?

asdasdasd · Answer

@lucaz  Can you please help me?

lucaz · Answer

long division helps you to factor the polynomial, you get something like
f(x)=(x+a)(x-b)(x+c)
the roots would be -a, b and -c

asdasdasd · Answer

Okay

lucaz · Answer

for example f(x)=x^3+5x^2-2x-24 factoring by long division you get
f(x)=(x+3)(x-2)(x+4)

asdasdasd · Answer

But isn't long division like x2–2x+4 by x–6.

asdasdasd · Answer

okay

lucaz · Answer

yes that's long division..

asdasdasd · Answer

x^2-2x+4*

lucaz · Answer

asdasdasd · Answer

Okay i understand now.

asdasdasd · Answer

How about synthetic division?

lucaz · Answer

they have the same goal, the operation is just a bit different

lucaz · Answer

you find the same result

asdasdasd · Answer

Can you give me an example of synthetic?