How to Solve Polynomials Warm-up Facts to know
... 9. The factorizations of x3 ± y 3 on the other side of the page have their generalizations. (a) Similarly to the factorization of x3 − y 3 , you can factor x − y out of xn − y n for any n. (Why?) What is the resulting identity? (b) Similarly to the factorization of x3 + y 3 , you can factor x + y ou ...
... 9. The factorizations of x3 ± y 3 on the other side of the page have their generalizations. (a) Similarly to the factorization of x3 − y 3 , you can factor x − y out of xn − y n for any n. (Why?) What is the resulting identity? (b) Similarly to the factorization of x3 + y 3 , you can factor x + y ou ...
Notes on Vector Spaces
... 1. If V is any vector space, V is a subspace of V ; the subset consisting of the zero vector alone is a subspace of V , called the zero subspace of V . 2. If F n , the set of n-tuples (x1 , x2 , ..., xn ) with x1 = 0 is a subspace; however, the set of n-tuples with x1 = 1 + x2 is not a subspace (n ≥ ...
... 1. If V is any vector space, V is a subspace of V ; the subset consisting of the zero vector alone is a subspace of V , called the zero subspace of V . 2. If F n , the set of n-tuples (x1 , x2 , ..., xn ) with x1 = 0 is a subspace; however, the set of n-tuples with x1 = 1 + x2 is not a subspace (n ≥ ...
