12
AssignmentMultiple Choice

Addition and Subtraction of Polynomials

Question 12 • FL-1200330-Algebra 2 CR

Which example illustrates the associative property of addition for polynomials?

Answer
A
[(2x2 + 5x) + (4x2 – 4x)] + 5x3 =(2x2 + 5x) + [(4x2 – 4x) + 5x3]
B
[(2x2 + 5x) + (4x2 – 4x)] + 5x3 =[(4x2 – 4x) + (2x2 + 5x)] + 5x3
C
(2x2 + 5x) + [(4x2 – 4x) + 5x3] =(2x2 + 5x) + [5x3 + (4x2 – 4x)]
D
[(2x2 + 5x) + (4x2 – 4x)] + 5x3 =[(5x + 2x2) + (–4x + 4x2)] + 5x3

Explanation

The associative property changes the grouping of addends without changing their order: (a + b) + c = a + (b + c). Choice A changes the grouping of the three polynomial expressions while keeping them in the same order. The other choices either switch the order of addends, which illustrates commutativity, or reorder terms within the polynomials.

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