3) Let Z, be ring integers mode 5 and f(x) € Zg(x) such that f(x)=x² + 2x + 1 then a) f(x) has only one root. b) f(x) has only two roots. c) f(x) irreducible polynomials.. d) No one of above.

Q: Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For…

A: We will use repeated differentiation to prove this

Q: Which of the following are continuous and piecewise polynomials with respect to the nodes o, x1, x2,…

A: Continuous and pocewise continuous of the polynomial

Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

A:

Q: LET b₂= SHOW THAT faxi) - faxo). (x₂-xo) f (x₂) - fcxo)_ _faxi) - faxo) (x₂-x₁) (x₂-x₁) (X₁-Xo)…

A:

Q: Find that a Polynomial function given Zeros. 5, 77, -8.

A: Given zeros,  0, 7, -8

Q: Find all zeroes of f (x) = 4x* – 3x² – x. Check all that apply. - O A) 1 O B) 2 + i C) _ 2 O D) 2 O…

A: Solving the problem by finding the zeros of the function.

Q: Fourth differences (i.n.b) First differences Second differences (in.b)| Third differences (i.n.b)…

A: x y First Difference Second Difference Third Difference Fourth Difference -3 -26         -2…

Q: 10. Show that the polynomial p(x)=x²-3x³-x² - 4x-20 has at least two distinct roots (Hin use the…

A: We have given,   f(x) = x4 - x2 - 4x - 20

Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

A:

Q: 4. For the function f(x) x+ 8x + 5x2-38x + 24, use long division to determine whether each of the…

A:

Q: Let H(x)= " plays hockey". Let B(x) = "x plays basketball". Which statement below means "If everyone…

A:

Q: A real number is called algebraic if it is a root of an algebraic equation f(x) = 0, where f(xo) ao…

A:

Q: Part A: Identify the zeros of the following polynomial function: f(x) = -x(x + 2)(x – 2)(x + 1)

A: Givenf(x) = -x(x+2)(x-2)(x+1)

Q: Determine the domain of a) ({x|x-1xR}) x-4 2x+2 f(x)=; ({x/x = −1,x = R}) c) ({x|x*1,xER}) Od) {x/x…

A: