2018 UNCO Math Contest II Problems/Problem 6

Problem

Circling the square. Exactly one of these polynomials is a perfect square; that is, can be written as $(p(x))^2$ where $p(x)$ is also a polynomial. Circle the choice that is a perfect square, and for that choice, find the square root, the polynomial $p(x)$.

(A) $36-49x^2 + 14x^4$

(B) $36-48x^2 + 14x^4-x^6$

(C) $9-12x + 4x^2 + 12x^3-8x^4 + 4x^6$

(D) $36-49x^2 + 15x^4-x^6$

Solution

$C; p(x) = 2x^3-2x + 3$

See also

2018 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All UNCO Math Contest Problems and Solutions
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