Prove all real polynomials of degree $n(n \geq 1)$ can be factorized to the product of k linear factors and l quadratic factors
97652
Can every real polynomial be factored up to quadratic factors?
31544
How to prove that this polynomial is larger than another for positive reals?
121404
How to factor polynomials in $\mathbb{Z}_n$?
55119
Proof that the coefficients of a polynomial are real
69523
Prove that polynomial of degree $4$ with real roots cannot have $\pm 1$ as coefficients (IITJEE)
133384
Question regarding to canonical factorization of $n!$?
89381
Prove that a real polynomial $x^n+ a_1x^{n-1}+ \cdots a_n$ cannot be completely resolved into linear factors if $a_1^2<a_2$.
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
109102
Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
76955
Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros
71572
factor-square property (FSP) of polynomials
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
134699
Can *any* real polynomial be factored linearly (plus a constant) over $\mathbb{R}$?
136077
Prove that $x-1$ is a factor of $x^n-1$
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $