1. Consider the following polynomials over Zs, where a is written for [a] in Zs: f(r) = 2x3 + 7x+4, g(x) = 4x2 + 4x + 6, h(x) = 6x2 +3 Find each of the following polynomials with all coefficients in Zs. (a) f(x)+ g(x) (b) g(x)h(x) (c) f(r)g(x) + f(x)h(x)

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: 4. For the following polynomial write the polynomial in standard form and specify: a) its degree b)…

A: Expand the polynomial then answer the questions.

Q: (10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of…

A:

Q: Let f(x) and g(x) be cubic polynomials with integer coefficientssuch that f (a) = g(a) for four…

A: Consider

Q: Below are two Lagrange interpolating polynomials, L₁ and L2. Following these are interpolating poly-…

A: For the first Lagrange polynomial, the points are:  x0=2,x1=5,x2=6,x3=8 Now,…

Q: We say that two polynomials f and g are equivalent over GF (p) if f(x) = g(x) for every x = GF (p).…

A: As per guidelines, I can do only first three subparts of the question.

Q: Determine whether the following polynomials are even, odd, or neither. (A) f (x) = 5a – 2a- 4x + 1…

A:

Q: 1. Identify the degree, end behavior and roots (w (a) f(x) = r³(x + 1)²(x² + 9)(x² – 4) - (b) /(x) =…

A: Degree of polynomial is the highest power of 'x' on polynomial equation Roots are found when f(x) =…

Q: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4…

A: Find second order Lagrange interpolation polynomial

Q: Let f(x) = 4x4+x3+2x+1 and g(x) = 3x2+2x+3 be two polynomials in Z5[x].  Determine the quotient and…

A: We have to solve given problem:

Q: 1. Let P be a polynomial where P(x) = (x + 6) (x+3)(x - 5). a. Rewrite the polynomial in standard…

A:

Q: Suppose f (x) = p(x)/q(x) , where p and q are polynomial functions with no common zeros. For what…

A: