1987 AMC 12 Problem 1

Attempt Problem 1 of the 1987 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 1987 AMC 12 solutions, or check the answer key.

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

(1+x^2)(1-x^3)

equals

1-x^5

1-x^6

1+x^2-x^3

1+x^2-x^3-x^5

1+x^2-x^3-x^6

Distribute each term of the first binomial across the second

The product

x^2(-x^3)

contributes the highest-degree term

Expanding gives

\begin{aligned} (1+x^2)(1-x^3) &=1+x^2-x^3\\ &\qquad-x^5. \end{aligned}

Thus the correct answer is D.

Problem 1 in other years