query: $\cos(nx)=Q_n(\cos(x))$ for polynomial $Q_n$ of degree $n$
positive_passages.docid: 148632
positive_passages.text: How to expand $\cos nx$ with $\cos x$?
negative_passages.docid: 84697
negative_passages.text: Show that if $|f(z)| \leq M |z|^n$ then $f$ is a polynomial max degree n
negative_passages.docid: 111248
negative_passages.text: The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
negative_passages.docid: 133101
negative_passages.text: Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
negative_passages.docid: 3036
negative_passages.text: Is a polynomial equation of degree $\ge 5$ not solvable by any way?
negative_passages.docid: 83036
negative_passages.text: f(g(x)) has a degree divisible by n
negative_passages.docid: 103238
negative_passages.text: Conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$ and irreducibility of $x^4 -22x^2+1$ (for minimal polynomial)
negative_passages.docid: 152347
negative_passages.text: Proof that a certain entire function is a polynomial
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 156597
negative_passages.text: Proving a reduction formula for the antiderivative of $\cos^n(x)$
negative_passages.docid: 83291
negative_passages.text: Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
negative_passages.docid: 158156
negative_passages.text: Finding the dual basis for the space of polynomials of degree $\leq$ 2
negative_passages.docid: 40426
negative_passages.text: Polynomial degree 3 Equation
negative_passages.docid: 121304
negative_passages.text: Is the set of polynomials of degree less than or equal to $n$ closed?
negative_passages.docid: 129834
negative_passages.text: Show that there is a unique polynomial of degree at most $2n+1$ such that $q^{[k]}(x_1)=a_k,$ $q^{[k]}(x_2)=b_k$ for $k=0, \dots, n$.
negative_passages.docid: 148813
negative_passages.text: Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
negative_passages.docid: 66960
negative_passages.text: Find a polynomial f(x) of degree 5 such that 2 properties hold.