3. Find a GCD of and in the ring Q[x]. 10-3x+3x8-11x7 +11x6 – 11x5+ 19x4 - 13x³ +8x² - 9x+3 26-3x+3x-923 +5x2-5x+2
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![3. Find a GCD of
and
in the ring Q[x].
10-3x+3x8-11x7 +11x6 – 11x5+ 19x4 - 13x³ +8x² - 9x+3
26-3x+3x-923 +5x2-5x+2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a13d6f1-c936-4abe-8bb4-18aaeeba508a%2F9d6a45a0-3c39-403c-925a-eea029fc4e7f%2F9l5lq4_processed.png&w=3840&q=75)
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- Show that the polynomial x 4p +xAq+1+x²r+2 3 divisible by x³ + x² + x + 1, where p, q, r, se N. + x4s +3 isThe characteristic of the ring 6x8 x 14 is (A) 2 (B) 48 (C) 84 (D) 1681. Compute the resultant of x polynomials have a common factor in Q[x]? Explain your reasoning. - 3x* – 2x + 3x² + 7x + 6 and x +x² + 1. Do these
- Determine which of the polynomials below are irreducible over Q. (a) a + 9x* + 12r² + 6 (b) x +x +1 (c) a* + 3x2 + 3 (d) r + 5x² + 1 (e) + r + 153 + a² + 6x + 14Let a and b be two integers such that gcd(a, b) =2. What is gcd(7a + 5b, 3a + 2b)? Show your work.Which of the following polynomials go to negative infinity as x approaches infinity and go to negative infinity as x approaches negative infinity? a) –3x3 + 9x² + 18x – 18 b) 5x208 – 39x51 +3 c) 128x7 – 64x6 + 32x5 – 16x4 + 8x³ – 4x² + 2x 1 O d) –x4 + 209