Question

given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = (p(x) + q(x)) + r(x)
to verify the associative property of addition, begin by finding the sum of the polynomials:
(3x + 4) + ((5x² - 1) + (2x + 6))
= 5 x² + 5 x + 9
complete
which equivalent expression would you set up to verify the associative property of addition for (3x + 4) + ((5x² - 1) + (2x + 6))?
○ (3x + 4) + (5x² - 1)
○ (5x² - 1) + ((3x + 4) + (2x + 6))
○ ((3x + 4) + (5x² - 1)) + (2x + 6)
○ (3x + 4) + (5x² - 1) + (2x + 6)
done

Explanation:

Step1: Recall Associative Property

The associative property of addition for polynomials \( p(x)+(q(x)+r(x))=(p(x)+q(x))+r(x) \). Here, \( p(x) = 3x + 4 \), \( q(x)=5x^2 - 1 \), \( r(x)=2x + 6 \).

Step2: Apply the Property

We need to rewrite \( (3x + 4)+((5x^2 - 1)+(2x + 6)) \) in the form \( (p(x)+q(x))+r(x) \), which is \( ((3x + 4)+(5x^2 - 1))+(2x + 6) \). The other options: first is missing \( r(x) \), second changes the order (associative is about grouping, not order), fourth is just removing parentheses without proper grouping for verification.

Answer:

C. \(((3x + 4)+(5x^2 - 1))+(2x + 6)\)