1980 AMC 12 Problem 2

Attempt Problem 2 of the 1980 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1980 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

2.

The degree of (x2+1)4(x3+1)3(x^2+1)^4(x^3+1)^3 as a polynomial in xx is
55
77
1212
1717
7272
Answer: D
Concepts:polynomialexponent
Small hint:
Find the highest power contributed by each parenthesized factor
Big hint:
Degrees add when nonzero polynomials are multiplied
Solution:
The first factor has degree 2⋅4=8,2\cdot4=8, and the second has degree 3⋅3=9.3\cdot3=9. Their product therefore has degree 8+9=17.8+9=17.
Therefore, the correct answer is D.
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