# Tagged Questions

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### prove for p(x) which is a quadratic polynomial

$p(x)$ is a quadratic polynomial . Prove that any given number for $a$ with one exception , we can find a number $b$ such that $p(a)=p(b)$ and $a$ is not equal to $b$.
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### Expressing $x^5-2x^3+6x^2+1$ as a sum of powers of $x+2$

I found this question in one old calculus exam on my university. It's simple enough: Express $x^5-2x^3+6x^2+1$ as a sum of powers of $x+2$ Now, this seems like a straightforward (although ...
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### Product property for reversing coefficients for polynomials

Given a polynomial $$P(x)=a_0+a_1x+\cdots+a_nx^n,$$ define $$f(P(x))=a_n+a_{n-1}x+\ldots+a_0x^n.$$ How can we prove that $$f(P(x))f(Q(x))=f(P(x)Q(x))?$$ Expanding out the expression should be ...
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### Question about Polynomial Factor Theorem

I was reading the solution to an algebra problem but got stuck at one part. Problem is here: (http://math.la.asu.edu/~ifulman/mat194/problem-solving.pdf) Example 4.2.6 -- page 140 of the PDF (the book ...
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### Find all the Zeros of the function? [closed]

Can someone find the zeros of the function and identify if each zero is rational of irrational? Please... I need this to pass the class. :(
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### How to solve this equation with linear n as well as polynomial n?

I am banging my head against the wall, but somehow I can't find a closed form solution to this equation in n: $$229,244 + 58,044 \cdot n = 130,000 * 1.78^n$$ Obviously, if there was no $n$ ...
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### Why isn't $y=(x^6)^{1/3}$ a polynomial function?

I've been told that $y=(x^6)^{1/3}$ isn't a polynomial function because of the radical but I believe that the equation could be simplified to $y=x^2$ which fits the definition of a polynomial ...
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### polynomial with an irrational expression of the free term

I have problem with solving: $x^3-2x-4\sqrt{6}=0$ I have no idea how to solve it. I transform it to $x(x-\sqrt{2})(x+\sqrt{2})=4\sqrt{6}$ but I'm stuck here
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### Simplifying Polynomials using Formulas

Am doing an 8th grade math text book, and I came across this one: If $h(y) = y^2$, and $g(z) = z^3$, HCF of $h(b) - h(a)$ and $g(b) - g(a) =$ ? I got to know $h = y$ and $g = z^2$, but couldn't do ...