(12) Let f(x) = 17x5 + 3x + 2x +9 and g(x) = x³ + 2x - 1. (b) Compute the quotient and remainder when f(r) is divided by g(x) in the ring Z/7Z.

Q: Find the inverse of X + (X² – 8X + 7) in the form aX + b in the ring Q[X]/(X² – 8X + 7). - a b =…

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Q: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

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Q: 3. Let p(x) = 6xª – 13x³ + 13x² – 2. - (a) Find q(x) such that p(x) = (2x – 1)q(x) using synthetic…

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Q: 1. Express the polynomial f(x) = 4x3 – 5x2 + 2x – 3 as a power of x + 2.

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Q: Let f(x)= x³ + 2x+ 1 and g(x)= 4x + 1 be two polynomials in a ring (Zs[x],+ ,.). Find q(x) and r(x).

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Q: Express as a polynomial. (4x - 3y)(x - 5y)

A: Given: (4x - 3y)(x - 5y)

Q: Determine which of the polynomials below are irreducible over Q. (a) a" + 9xª + 12:r² + 6 (b) a* + x…

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Q: consider two polynomials P(x) =6x+1 and Q(x)=4x2-3x+2 carry out the indicated operation and simplify…

A: Explanation of the solution is given below...

Q: Write g(x) = x² + x³ + 2x²+x+2 as a product of irreducible polynomials over 2.₂. за

A: Write as a product of irreducible polynomials over .

Q: Multiply the polynomials (x-1)(x* +x³ + down an identity for (x - 1)(x" +x"-1 +..+x² +x + 1) for n a…

A: Multiply the given polynomials using table (x-1)(x4+x3+x2+x+1)   x4 x3 x2 x 1 x x5 x4 x3 x2 x…

Q: 4. Write the polynomial in standard form. * 4g – g° + 3g² – 2 -2 +4g + 3g – g g - 3g +4g - 2 O A -g…

A: Standard Form of Polynomial states that the polynomials needs to be written with the exponents in…

Q: Solve the polynomials 3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

A: Given polynomial,  3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

Q: Open with 1.9.1 Dividing Polynomials conmuer (Conthua Using the previous example, complete the…

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Q: 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |

A: Start with Right hand side as follows.

Q: (4) Find a polynomial that has 1+i and 1- i as zeros.

A: We have to find polynomial

Q: Find the unique quotient q(x) and remainder is divided by g(x). Consider polynomials in What #f(x) =…

A: Solution: f(x)=2x4+x2-x+1g(x)=2x-1 To find the quotient and remainder we use long division method.

Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

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Q: Find a value for c so that the polynomial y^2+10y+c factors to (y+5)2.

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Q: Determine whether or not the given polynomial is irreducible over Q (a) x4 - 10x² + 1 (b) (5/2)x+…

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Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…

Q: Determine the number a in Z5 so that (x - a) becomes a divisor of f (x) = x ^ 3 + 2x ^ 2 + 3x + 3 in…

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