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# Polynomial

Given $$P$$ is a polynomial that is not constant, satisfy $$P\left( P(x) \right) = (x^2 + x +1) \times P(x)$$ for every real $$x$$. Find $$P(10)$$.

Note by Fidel Simanjuntak
3 months, 2 weeks ago

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Hint: Let $$d$$ denote the degree of polynomial $$P(x)$$, then the degree of LHS is $$2d$$, and the degree of RHS is $$d+2$$. So can you solve for $$d$$? And can you determine the function $$P(x)$$?

- 3 months, 2 weeks ago

I got $$P(x) = x^2 + x$$ but I dont know, maybe there's another possible formula for $$P(x)$$

- 3 months, 2 weeks ago

No, there isn't. If you try for (constant of quadratic polynomial not equal 0), then you get a system of equations that has no solution.

I know that this isn't the best/fastest way to get the answer, but it works!

- 3 months, 2 weeks ago