f(x) =2x^5+x^3+1 a=-2
We need to find f(-2)
Needed is the value of x which solves the equation
2x^5+x^3+1= - 2
which we can write as:
Using polynomial division it is easy to show that:
x^5+1= (x+1) ( x^4-x^3+x^2-x+1)
x^3+1= (x+1) (x^2-x+1) ( in fact there is similar formula for any odd n for x^n+1)
Thus (x+1) factors out of the equation and we can set
and one of the possible solutions is
There could be 4 more solutions (in this case they are complex) but we'll not work them out here.
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