is there a method to finding factors when factoring a polynomial ?

Question

anonymous · Answer

there is no exact method
but if possible find all the roots
then (x-each root) is a factor of the given polynomial

espex · Answer

I would say that there is. One method that I like to use is to write the polynomial and braces, then fill in the blanks: $$x^2-4x+4 \space\space\space\space(\space\space\space)(\space\space\space)$$
Then it's just a matter of looking to see what two items give me the first term, the last term and if I can add them together to get the middle term.

anonymous · Answer

quess I don't follow you

anonymous · Answer

That was to  eSpex

espex · Answer

What does it take to get x^2? I would say x * x, so in my example I would the write: $$x^2-4x+4 \space\space\space\space\space\space(x\space\space\space)(x\space\space\space)$$ Then I would look at the last term, what does it take to get 4: 1 4, 2 2 If I add 2 and 2 together I get the middle term, 4, but I need a negative so I would fill in $$x^2-4x+4 \space\space\space\space\space\space(x-2)(x-2)$$  After which I would foil to check my work.

anonymous · Answer

Thank you

espex · Answer

You're welcome. Hope you find it useful.