Answer: Division (choice B)
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If you add the two polynomials, you get
(6x^2-2)+(6x^2+2) = 12x^2
which is another polynomial.
We can rule out choice A.
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If you subtract the polynomials, the same kind of story happens (but you'll get a different polynomial)
(6x^2-2)-(6x^2+2) = -4
The term -4 is a polynomial of degree 0.
We can rule out choice D.
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If you multiply the two polynomials, then you get another polynomial. Use the FOIL rule
(6x^2-2)(6x+2) = 36x^2 + 12x - 12x - 4 = 36x^2 - 4
or you could use the difference of squares rule to help expand
(6x^2-2)(6x+2) = (6x)^2 - (2)^2 = 36x^2 - 4
or you could use the box method (see Figure 1 in the attached images below)
Whichever method you use, the result is 36x^2 - 4 which is another polynomial.
We can rule out choice C. The only thing left is choice B.
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When dividing two polynomials, it is not always guaranteed to get another polynomial as a result. Use polynomial long division to calculate (6x^2-2)/(6x^2+2) and you'll get what you see in Figure 2 below. Figure 3 shows the long division table for (6x^2+2)/(6x^2-2). Both figures 2 and 3 show a nonzero remainder. The nonzero remainder means the result is not a polynomial.
