1980 AHSME Problems/Problem 2

Problem

The degree of $(x^2+1)^4 (x^3+1)^3$ as a polynomial in $x$ is

$\text{(A)} \ 5 \qquad \text{(B)} \ 7 \qquad \text{(C)} \ 12 \qquad \text{(D)} \ 17 \qquad \text{(E)} \ 72$

Solution 1

It becomes $(x^{8}+...)(x^{9}+...)$ with 8 being the degree of the first factor and 9 being the degree of the second factor, making the degree of the whole thing 17, or $\boxed{(D)}$

Solution 2

First note that note that $deg(P(x))^n = ndeg(P(x))$ and that $deg(P(x)Q(x)) = deg(P(x))+deg(Q(x))$ .

1980 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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1980 AHSME Problems/Problem 2

Contents

Problem

Solution 1

Solution 2

See also