(a) Determine whether the polynomials 1+ 3x + 3x?, x + 4x?, 5 + 6x + 3x², 7+ 2x – x² linearly dependent or linearly independent in P2

Q: Q2/ Fit a second - order polynomial to the data in the following table: X 5 1 4 Y 2 3 4 -1 4 76 O 00…

A: When a equation has one degree then it is known as linear equation. If the equation has two degree…

Q: Find necessary and sufficient conditions on the numbers a, b, c E R under which the polynomial xª +…

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Q: 3 3x2+2x+1 3. Compute dr 2 x2

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Q: find the 2003 quotiont 40+ 3 when divPde polynomial by c+ I

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Q: e down a polynomial of degree exactly 4 that interpolates the four points: (-1,-5 1), (2, 1), (3,…

A: We have to find the polynomial equation from given points.

Q: 14.) Factor each polynomial using the factor theorem. a) x - 5x2 - b) 2x3 + x2 - 27x- c) 3x 22x 16 -…

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Q: Q2/ Fit a second - order polynomial to the data in the following table: 5 1 4 7 Y 2 8 3 4 -1 4 6 00

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Q: Identify the end behavior for the following polynomial a) ↑↑ 个个 8r7 +5x³2x² + 1 此 b) ↓ c) ↑↓ d) ↓↑

A: Given function fx=8x7+5x5-2x2+1 Identify the end behaviour of the polynomial.

Q: 10. Which of the following polynomials is NOT divisible by (3x+ 1)? A. 6x2 + 17x+ 5 B. 3x - 4x2+…

A: Use remainder theorem

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: Determine whether the following polynomials span P2. P1 =4 -x+3x2, p2 = 4 + x, p3 = 24 + 2x + 6x2,…

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Q: 6. Factor each polynomial using the factor theorem.1 3- 3x2. 10x + 24 d) 4x* + 7x e) x - 5x – 7x³ +…

A: We find out the factors of the given polynomials.

Q: Divide the following polynomials k- 4k* - 3k - 5k + 6k – 3

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

Q: 6. Verify whether two polynomials with real coefficients Xª+X-2 and X3+2X –3 are relatively prime or…

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Q: 11. Factor the following polynomials: a) x²-4x-5 b) x²+10x+25 c) x3 +64 d) 10x219x - 15 e)…

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Q: Choose the polynomial that is written in standard form. A7x + 8x8+2 7x -3x¹y + 2x²y² + 5y³ 10xy +…

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Q: Use long division to divide the following polynomials: (3ct + a3-#+1) 은 (22-2x + 1) O 3a2-5x +12 +…

A: Answer

Q: Check whether or not x³ + 2x + 1 € F5[x] is a primitive polynomial.

A: Primitive polynomial

Q: 3. Find the greatest common divisor of: (a) The polynomials r³ + x² + x and r³ +x* +x² + x in Z2.

A: The given polynomials are: x3+x2+x, x5+x4+x2+x The given group is ℤ2.

Q: 2. Find the interpolating polynomial using NDD of the points (0,0) , (1,16) , (2,48), (4,88) and…

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Q: It is possible to write xk as a linear combination of Chebyshev's polynomials, for example %3D…

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