p : R → R p : x ↦ p ( x ) {\displaystyle p:\mathbb {R} \to \mathbb {R} \quad p:x\mapsto p(x)}
R {\displaystyle \mathbb {R} }
N {\displaystyle \mathbb {N} }
N Q C Z R {\displaystyle {\mathbb {N} }{\mathbb {Q} }{\mathbb {C} }{\mathbb {Z} }{\mathbb {R} }}
a 2 ( o ) {\displaystyle a_{2(o)}}
n = ± a n − 1 a n − 2 … a 1 a 0 ( o ) {\displaystyle n=\pm a_{n-1}a_{n-2}\ldots a_{1}a_{0(o)}}
0 ≤ a k ≤ o − 1 {\displaystyle 0\leq a_{k}\leq o-1}
( p n + q m ) ( x ) = ∑ k = 0 n a k x k + ∑ l = 0 m a l x l = ∑ k = 0 max ( m , n ) ( a k + b k ) x k {\displaystyle (p_{n}+q_{m})(x)=\sum _{k=0}^{n}a_{k}x^{k}+\sum _{l=0}^{m}a_{l}x^{l}=\sum _{k=0}^{\max(m,n)}(a_{k}+b_{k})x^{k}}
( c ⋅ p ) ( x ) = ∑ k = 0 n c a k x k , c ∈ R {\displaystyle (c\cdot p)(x)=\sum _{k=0}^{n}ca_{k}x^{k},c\in \mathbb {R} }
( p n ⋅ q m ) ( x ) = ( ∑ k = 0 n a k x k ) ⋅ ( ∑ l = 0 m b l x l ) = ∑ k = 0 n ∑ l = 0 m a k b l x k + l = ∑ i = 0 n + m ( ∑ k + l = i a k b l ) x i {\displaystyle (p_{n}\cdot q_{m})(x)=\left({\sum _{k=0}^{n}a_{k}x^{k}}\right)\cdot \left({\sum _{l=0}^{m}b_{l}x^{l}}\right)=\sum _{k=0}^{n}{\sum _{l=0}^{m}a_{k}b_{l}x^{k+l}}=\sum _{i=0}^{n+m}{\left({\sum _{k+l=i}^{}a_{k}b_{l}}\right)}x^{i}}
x 2 ≥ 0 forall x ∈ R {\displaystyle x^{2}\geq 0\qquad {\textrm {forall}}x\in \mathbb {R} }
a → A B → {\displaystyle {\vec {a}}\quad {\overrightarrow {AB}}}
≤ {\displaystyle \leq }
I n s e r t f o r m u l a h e r e {\displaystyle Insertformulahere}
B = c {\displaystyle {\mathcal {B}}=c}
Polynomial of degree 2: f(x) = x2-x-2=(x+1)(x-2)
Polynomial of degree 3: f(x) = x3/5+4x2/5-7x/5-2=1/5 (x+5)(x+1)(x-2)
Polynomial of degree 4: f(x) = (x+4)(x+1)(x-1)(x-3)/14+0.5
Polynomial of degree 5: f(x) = (x+4)(x+2)(x+1)(x-1)(x-3)/20+2
