Let P, Q = Z/2Z[x] be the following polynomials: P = x² + x³ + x² + x, Q = x³ + x. Divide P by Q with the remainder: find polynomials S, R € Z/2Z[x] with deg R degQ such that P = QS + R.

Divide the polynomials using long divisions.

Let R² have the inner product (u,v) = 5u₁V₁ + 4u₂V2, and let x = (2,2) and y = (4, − 1). a. Find ||x, y, and (x,y) |². b. Describe all vectors (z₁,z₂) that are orthogonal to y. a. Find ||×||, ||y||, and | (x,y)|². ||x|| = (Simplify your answer. Type an exact answer, using radicals as needed.) (Simplify your answer. Type an exact answer, using radicals as needed.) = |||| | (x,y) |² = (Simplify your answer.) b. Describe all vectors (z₁,z₂) that are orthogonal to y. Choose the correct answer below. O A. All multiples of (-1,5) are orthogonal to y. B. All multiples of (1,5) are orthogonal to y. C. All multiples of (1, −5) are orthogonal to y. D. The zero vector is the only vector orthogonal to y.

7y5 – 3y3 + 10y – 11y3 – 19y2 + 2y List down the pairs of like terms for the given polynomial.

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