[Answer] What is the additive inverse of the polynomial -9xy2 + 6x2y - 5x3?

Answer: 9xy2 - 6x2y + 5x3

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What is the additive inverse of the polynomial -9xy2 + 6x2y - 5x3? Add the terms of each column. The additive inverse of the polynomial x2 + 3x + 2 is – (x2 + 3x + 2). This is equivalent to the additive inverse of each of the terms. – (x2 + 3x + 2) = – x2 – 3x – 2 To subtract two polynomials add the additive inverse of the second polynomial to the first. 5x3 7x2 x 5 13x3 7x2 9x 6 Add the terms of each column. 5 10.1 Adding and Subtracting Polynomials The additive inverse of the polynomial x2 3x 2 is (x2 3x 2). This is equivalent to the additive inverse of each of the terms. (x2 3x 2) x2 3x 2 To subtract two polynomials add the additive inverse of the second polynomial to the first. 6 If we write a polynomial as p(x)=anxn +an1xn 1 +··· a1x a0 where an 6=0 then n is the degree of p(x) an is the leading coecient of p(x) and anxn is the leading term of p(x). For example the leading coe 3cient of 4x 5x2+6x7is4.Itsdegreeis3 and its leading term is 4x3. Add the opposite of the second polynomial to the first polynomial. The opposite (or additive inverse ) of a real number a is a. Similarly if A is a polynomial then A is its opposite. ... 6x2y 1 x2y2 1 2xy2 5 3 5x2y 2xy 8 ... 34. 1 8x3 6x 72 1 5x3 2x 42 35. COMPUTATIONAL COMMUTATIVE ALGEBRA NOTES 5 R[x] (addition and multiplication are just the standa...

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