+118723 $$(1)\qquad (x+1)(x+3)(x+5)(x+7)+15$$
http://www.wolframalpha.com/input/?i=%28x%2B1%29%28x%2B3%29%28x%2B5%29%28x%2B7%29%2B15
I am just thinking about how to do this without the help of an online calc.
You will need to use the remainder theorum.
You have to look for a value of x that will make that expression = 0
hence (x+1)(x+3)(x+5)(x+7) must equal -15
for this to be true an odd number of them must be negative, which means x must be negative but bigger than -7.
I know x will not be -1,-3,-5, or -7 because they will make the expression = 0 (NOT -15)
try -2
-1*1+3*5=-15
so (x+2) is one factor.
try -4
-3*-1*1*3 no no good
try -6
-5*-3*-1*1=-15 good
so (x+2)(x+6) is a factor
Now I do not know if there is an easier way but I would expand and simplify the original question
then I would divide by x^2+8x+12
And then i would find the next factor.
does that make sense.
