College Algebra: reviewing for Final Exam!
If the number 3 is a zero of a polynomial function f(x), then which of the following is true?
a.) x-3 is a factor of f(x)
b.) x+3 is a factor of f(x)
c.) -3 is a zero of f(x)
d.) f(-3)=0
Can someone help me answer this question and understand polynomials?

Question

bahrom7893 · Answer

I'm not going to go into too much details regarding polynomial functions, basically they're some functions the equation of which looks like this:$$f(x)=a*x^n+b*x^{n-1}+c*x^{n-2}....+some \space constant*x+some \space constant$$

p0sitr0n · Answer

x-3 is a factor

bahrom7893 · Answer

where all the powers are positive integers

p0sitr0n · Answer

By the fundamental theorem of algebra i believe, you can factor (x-r) out of any polynomial  that has root r

fibonaccichick666 · Answer

You would have to know there is a root of 3 though

fibonaccichick666 · Answer

oh, and we do haha

p0sitr0n · Answer

it is stated

bahrom7893 · Answer

Now, that may look a bit overwhelming, but here are a few simple examples:$$f(x) = x+1$$$$f(x)=x \space (which \space is \space the \space same \space as \space x+0)$$

fibonaccichick666 · Answer

^Note, that has a zero at x=-1

bahrom7893 · Answer

But stop giving the answers, I'm trying to explain here

anonymous · Answer

I'm reading @bahrom7893 don't worry. I'm reading each one of your comments. But I'm learning. Trying to comprehend what you're saying.

bahrom7893 · Answer

Another thing special about polynomials are their graphs.. you're probably very familiar with this one:$$y=x^2$$
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