Use the quotient remainder theorem and division into cases to show for all integers n, the integer n2 has a remainder of 0 or 1 when divided by 3.

Q: What is the smallest positive integer n such that 80325 divides n!

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Q: Find the product AB if

A: Given: A=12-340-2 and B=5-420-16317058

Q: divide x to the power 4 + x - 1 by x-1 in long division or synthetic

A: The given polynomial division is .We have to perform the given division.

Q: (а) 2,646 (b) 819 (с) 2,475

A: We have to find

Q: 9. Use the repeated subtraction view of division to find each quotient. Show all your work (at least…

A: Given, 3241÷43 now apply repeated subtraction method three times 3241-433198-433155-433112 final…

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

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Q: 4. Rewrite n with a fractional exponent

A: Given,

Q: Use long division to determine the decimal expansion of . You can either: 12 90 1) Show your work on…

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Q: says the remainder is wrong.

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Q: (a) Find the remainder when 30! is divided by 31.

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Q: Was the highest power of 23 that will divide 5000! without leaving a remainder? (a) (b) 714 (c) 276…

A: We need to find ,  highest power of  23 that will divide 5000!. We know , highest power  m of any…

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

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Q: Choose all the factor pairs of 54 O -3 and -18 2 and 27 6 and -9 7 and 8 -2 and 27 -6 and -9 -1 and…

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Q: 1. Arrange the terms of the dividend in descending powers x-3 ) 2x-3xe -x+ 4

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Q: Use the unique factorization theorem to write the following integers in standard factored form. (a)…

A: Unique Factorization Theorem. For every integer n>1, there exists a positive integer k and…

Q: Let a = -26, 6 = 12 For a divided by b, what is the integer quotient using the least nonnegative…

A: To find: The integer quotient and remainder using the least nonnegative remainder method and least…

Q: Divide (x5+2x4 - 2x² - 5x-12)÷(x²-3)

A: A long division of polynomials is an algorithm for the dividing polynomial by another polynomial of…

Q: The remainder upon the division of x98 +4 by x - 2 in z, is: 6. None

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Q: use the Euclid's division lemma to show that the cube if any positive integer is either of the from…

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

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Q: process

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Q: Find the remainder upon dividing 98! by 101.

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Q: The prime factorization of 2700 is given by: where a = 27002ª. 36.5c.7d A , b = A/ , C = A/,d=

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