1.
Factor completely the following expression: \(P(x)=x^4-5x^2+4\).
Treat as quadratic in \(x^2\): \(x^4-5x^2+4=(x^2-1)(x^2-4)=(x-1)(x+1)(x-2)(x+2)\). Answer: E
2.
Solve the following for the exact value(s) of x: \((x+3)^2=9\).
\(x+3=\pm3\). Thus \(x=0\) or \(x=-6\). Answer: C
3.
Write a polynomial with roots \(-1,1,2\).
Form \((x+1)(x-1)(x-2)=x^3-2x^2-x+2\). Answer: C
4.
Solve for x, \(P(x)=x^3+6x^2+3x-10=0\).
Test \(x=1\): root. Factor to \((x-1)(x+5)(x+2)\). Roots: \(-5,-2,1\). Answer: A
5.
Which of the following best describes the graph of polynomial of degree 6 with a negative leading coefficient?
Even degree means both ends same direction. Negative leading coefficient means both ends down. Answer: D
6.
Which graph best represents \(y=-x(x+3)^2(x-3)^3\)?
Degree \(6\) with negative leading coefficient gives both ends down. Multiplicities also match the shown graph. Answer: D
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