Answer:
(A) 8y^2 +8y -10
(B) 22y^3 +2y^2 +2y -7
(C) yes, for these polynomials. The result of adding or subtracting the polynomials in this problem is another polynomial, suggesting the set of polynomials is closed to addition and subtraction.
Step-by-step explanation:
A. (4y + 2y^2 − 3) + (−4 + 2y^2 + 2y) + (4y^2 − 3 + 2y)
= y^2(2 +2 +4) +y(4 +2 +2) +(-3 -4 -3)
= 8y^2 +8y -10 . . . . total length of sides 1, 2, 3
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B. The length of the 4th side is the difference between the perimeter and the sum of the other three sides:
(22y^3 + 10y^2 + 10y − 17) -(8y^2 +8y -10)
= 22y^3 +y^2(10 -8) +y(10 -8) +(-17 +10)
= 22y^3 +2y^2 +2y -7 . . . . length of 4th side
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C. The result of adding or subtracting the polynomials in this problem is another polynomial, suggesting the set of polynomials is closed to addition and subtraction. An example is not a proof, but there is nothing about this example that would suggest a different conclusion.
