Question 554003: (x-2)(x+1)(x+6)(x+9)+108=0
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! By inspection, I can see that there is a zero at x=0, and by graphing the function f(x)=(x-2)(x+1)(x+6)(x+9)+108, I can see that there is another zero at x=-7. There are two additional real roots that are probably irrational.
When I expanded the polynomial equation, I got x^4 +14x^3 +37x^2-84x=0. By factoring out the x, and then performing synthetic division by the known zero of x=-7, we can get the equation down to a quadratic, which can be solved by the quadratic formula. The quadratic equation turns out to be
x^2+7x-12=0. Solving this, I get  . For more details on this, send me an Email. I have some information on the TI84 Graphing Calculator on my website, and some explanations on synthetic division and polynomial functions on my website.
If you or anyone needs to contact me, my Email address is rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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