Let and . Define . Which of the following correctly describes…

MATHEMATICS · Single correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let p(x)=2x4−x2+3p(x)=2x^4-x^2+3 and q(x)=x3−4xq(x)=x^3-4x. Define r(x)=p(x)−q(x)r(x)=p(x)-q(x). Which of the following correctly describes r(x)r(x)? (a) degree 4, positive leading coefficient, even (b) degree 4, positive leading coefficient, neither even nor odd (c) degree 3, negative leading coefficient, odd (d) degree 4, negative leading coefficient, neither even nor odd

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