Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.

Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

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Q: 2. Expand by multiplying 'o) a) (3x+ 4)(2x - 2) b) (2x - 7)(-4x + 5) c) -4y(-4x -5y)

A: Given  a) (3x+4)(2x-2) Multiplying,  (3x+4)(2x-2) = (3x)(2x-2)+4(2x-2)…

Q: If a number has n fraction (n>1), then the square of the number has 2n factors is this true

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Q: find the product of 4 6/4×3 4/3

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Q: State the remainder theorem and the rational root theorem.

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Q: A rectangle has a width of 2x - 3 and a length of 3x + 1. a) Write its area as a simplified…

A: Given  Width w = 2x-3  Length l = 3x + 1  We need to find the area polynomial for the given…

Q: Suppose the product of 22 integers is equal to 1. Prove that their sum is not equal to 0.

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Q: A large tract of land is being surveyed and divided into smaller parcels for sale. When parcels of…

A: Given information:Parcels of  leave  leftover.Parcels of  leave  leftover.Parcels of…

Q: plz help out with these math questions. ANSWER IT WITH 7-8 PARAGRAPHS a) Describe the history of…

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Q: 2. Factor. 10 x2/5 (4x + 7)/2 +÷ 7 3 7/5 (4x + 7)-1/2 3

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Q: Divide the following polynomial by using long division and prove your sender by the remainder…

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Q: 0, the remainder is 2; and when divided by 11, the remainder is 0. remain is 5; when divided by

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Q: Simplify by removing factors of 1. 2 - 6z + 8 z* + 2z - 8

A: Simplify

Q: o the di

A: The division using the c-strips:

Q: II. Use the Remainder Theorem to find the remainder when each polynomial is divided by the…

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Q: 11. Express the following as a trinomial in simplest form in terms of the variable z. (z + n)" n=0…

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Q: 6h term of a G.P. is 9375 and its 4th term is 375. ind its 9th term.

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Q: Factor. z² - 4 © (z +^2)(z - 2) O (2- 2)2

A: We will have to use the difference of square formula  a2-b2=(a+b)(a-b)

Q: Which integers are quadratic residues of 11?

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Q: Suppose the second column of B is all zeros.  What can you say about the second column of AB?

A: If the second column of B is all Zeros, then the second column of AB will also be all Zeros.

Q: Use the quotient remainder theorem and division into cases to show for all integers n, the integer…

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Q: Find the 66th term of the triangular numbers {1, 3, 6, …}.

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Q: The digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 are to be filled into the boxes below and each digit can be…

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