Question 211810
1.  Creating a polynomial is simple.  Start with your factors.
{{{(x-4) (x+2)}}}  you can use any numbers you want for this.  At this point, you can choose the operation + or - that you want as well.  To get the polynomial, just FOIL.  (First, Inside, Outside, Last)
First:{{{x*x=x^2}}}; Inside:{{{-4*x=-4x}}}; Outside:{{{2*x=2x}}}; Last:{{{-4*2=-8}}}
So, the expression is:
{{{x^2-4x+2x-8}}}
Combine like terms:
{{{x^2-2x-8}}}  This is a polynomial and the factors are the ones you started with.

2. {{{x^2+8x+7}}} 
To factor, we are going to do the exact opposite of what we did in problem number 1.   Your first two numbers have to multiply to be {{{x^2}}} so there is only one choice.  It must be x*x.
(x(-+)?) (x(-+)?)

Next, to get the last numbers we need to find what adds to be 8 and multiplies to be 7.  Since 7 is a prime number, there is only one choice (1,7)
(x(-+)7) (x(-+)1)

Now choose the operation.  In this case, 7+1=8 and 7*1=7 so we will use the + operation in both factors.
(x+7) (x+1)