f = x² + x³x²+1, g = x³ + 1 in Q[x];

Q: Two polynomials are defined in MATLAB as >>p=[5 03 2 0]; q= 0 -1]; lo find the zeros of T(s) =…

A: Matlab is a programming and numerical platform to compute values, analyze , create model.

Q: Generate the 2nd and 3rd degree Legendre polynomials.

A: Since we know the Rodrigue's formula of Legendre polynomial is Pn(x)=12nn!dndxnx2-1n For second…

Q: In Z3[x], show that the distinct polynomials x4 + x and x2 + xdeterminethe same function from Z3 to…

A: We know that ℤ3 is a field i.e., a commutative ring with unity in which every non-zero element has a…

Q: F. Find the four roots of the polynomial z* + 16 and use these to factor z* + 16 into two quadratic…

A: We need to find the root of z4+16=0 Consider: z4+16=0⇒z4=-16⇒z22=-16⇒t2=-16…

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: In Z3[x], show that the distinct polynomials x4 + x and x2 + x determinethe same function from Z3 to…

A: Given: x4+x and x2+x are two distinct polynomials in ℤ3x.We need to show that the given two…

Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

A:

Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: Calculate the first three Legendre coefficients for f (x) = x² + 1 and then express the f(x) in…

A: The solution of the differential equations are the functions that satisfies the differential…

Q: B). Find the volume of the solid obtained by rotating the region bounded the given curves about the…

A:

Q: Write x3 + 2x + 1 as a product of linear polynomials over some extension field of Z3.

A: Given: x3+2x+1. To Do:We have to write x3+2x+1 as a product of linear polynomials over some…

Q: 2. Write the polynomial in standard form. * 5w – 2w + 2w - 8 2w + 2w + 5w-8 -2w + 2w -8+5w 5w - 2w +…

A: Steps :: 1) Write the term with the highest exponent first2) Write the terms with lower exponents in…

Q: The polynomial x2 - 2x - 3 is irreducible (over R). Select one: O True False

A:

Q: Find the standard inner product on P of the given polynomials. p= -2+ 4x + a2, q = 3+ 4x 3a2. (p, q)

A:

Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate…