1. In Z7[x], find q(x) and r(x) such that 53 1 (22r )r(a) and deg r(x) < 2. 1. In Z7[x], find q(x) and r(x)...
Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that q(20) = yo q(x1) = y1, and 9' (21) = y1 with xo < X1. Under what exact conditions is deg(q) = 2?
Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that q(20) = yo 9(x1) = yi, and d'(x1) = yi with x0 <21. Under what exact conditions is deg(q) = 2?
Find the solution to the interpolation problem of finding a polynomial q(x) with deg(a) <2 and such that q(20) = yo, q(x1) = y1, and d(x1) = yi with Zo < 21. Under what exact conditions is deg(q) = 2?
= Yo, Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and such that q(xo) q(x1) = yi, and q'(x1) = yi with Xo < X1. Under what exact conditions is deg(q) = 2?
Find solution to interpolation, and what exact conditions is deg (q) = 2? & Find solution to the interpolation problem of finding a polynomial 9x with deg (9) £2 and such that: 9(x) = Yo 4.X) PY q (x) = Yi with Xo LX. Under what exact conditions is deg (q) = 2?
Find the solution to the interpolation problem of finding a polynomial q(a) with deg(q) < 2 and such that q(20) = yo, q(x1) = yi, and q' (x1) = y; with Xo < X1. Under what exact conditions is deg(q) = 2?
Find irr(α, Q) and deg(α, Q), where α = √ 2 + i.
Definition A: Let R be ring and r e R. Then r is called a zero-divisor in Rifr+0r and there exists SER with s # OR and rs = OR. Exercise 1. Let R be a ring with identity and f € R[2]. Prove or give a counter example: (a) If f is a zero-divisor in R[x], then lead(f) is a zero-divisor in R. (b) If lead(f) is a zero- divisor in R[x], then f is a zero-divisor in R[2]....
2. Consider Z7 Prove that the operation on Z7 dened by [x]7 [y]7 = [5xy]7 is well dened. = 2. Consider Z- Prove that the operation ♡ on Z- defined by [2]7 0 [y]; [5xy]7 is well defined.
Suppose that the functions q and r are defined as follows. g(x)=-x+2 r(x)=x²+1 Find the following. (y - z)(-2) = 0 (20") (-2) = 0 x 3 ?