Let be the following set of rational numbers: Consider the algebraic structure (R2, +, ·), where + and · are the sum and product common between numbers. Briefly explain why (R, +, ·) is not a field.

Q: Let a be an odd integer. Show that (i) 8 | a2 − 1; (ii) 16 | a4 + 15.

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Q: Perform the indicated operations and write the result in standard form, √-12(√-4 - √2)

A: Given , -12-4-2         =-12.-4--12.2         =-12-4--122         =48--29         =42x3--1.4x6…

Q: Fill in the blank for this polynomial identity. a + b5 = (a + b) × A (a² + b²)² (a – b)?(a² – 2ab –…

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Q: Perform the indicated operations and write the result in standard form, (-6 - √-12) /48

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: 2. Simplify each polynomial. Gather like terms. a)-p +5q – 8r – q+ 3p+9r +1 c) 5q - 9s – 8r + 8q –…

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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: True or False: The degree of the following polynomial is 7: &x+&g. O True O False

A: Degree of polynomial with two variable It is the maximum degree of the degrees of the terms with…

Q: Remainder must always be either less than or equal to the divisor. true or false

A: Remainder must be either less than or equal to the divisor . The above statement is true .

Q: 21. Write the expression (x + 6)(x – 4) as a polynomial in standard form. A. x - 10x + 2 B. x + 10x…

A: To write the expression as a polynomial in standard form.

Q: let B= [-1 2 7 -3] Find -3B

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Q: Determine which expression is the correct rationalization of the numerator of Vx+1-5 x+ 24 x+1 +5 x-…

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Q: What degree is the monomial x to the third power?

A: Degree of a monomial is the sum of the exponents of all of its variables.

Q: Which property of real numbers is illustrated by the equationi shown below? Commutatnapraparty…

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Q: Perform the following operations. Express your answer as a positive or negative quotient of two…

A: Given query is to find the value of the expression.

Q: For each of the following rational expressions, determine the values for which the expression is…

A: We have given rational expression  (A)  7m20n The expression is undefined when denominator =0 n=0…

Q: write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7

A: Given problem:- write a polynomial in standard form that has the given zeros: 1,-2+√7, -2-√7

Q: d) (5x) + 5 – (0,25) +83 3. Use the laws to re-write the following expression as a power of x:

A: The given expression is xxxxx use the formula x=x12 , xaxb=xa+band simplify…

Q: What rational algebraic expression is the same as x² – 1 х — 1

A: The given expression is                               x2-1x-1 To find the rational algebraic…

Q: For the following polynomial, one zero is given. Find the remaining zeros. P(x)=x +7x - 144, 4i is a…

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Q: Expand and simplify each of the following algebraic expressions. b) (2)(3x – 6)(-3x + 4) a)…

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Q: A rational expression consists of a/an divided by a nonzero

A: Given : A rational expression consist of a / an _____________ divided by a nonzero ___________ .

Q: Find the product. Assume variables represent positive real numbers. 2) 2x2/5(x11/5-3x) A)2x13/5 -…

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