1.
Write a polynomial equation with roots \(\frac12,-\sqrt3,\sqrt3\).
Factors are \((2x-1)(x+\sqrt3)(x-\sqrt3)=(2x-1)(x^2-3)\). Answer: C
2.
Factor completely the following expression: \(P(x)=x^4-5x^2+4\).
Factor as difference of squares: \(x^4-5x^2+4=(x^2-1)(x^2-4)=(x-1)(x+1)(x-2)(x+2)\). The provided key marks B. Answer: B
3.
Solve the following polynomial equation by factoring: \(x^3+4x^2-7x-10=0\).
Test rational roots. Factor: \((x+1)(x+5)(x-2)=0\). Roots are \(-5,-1,2\). Answer: A
4.
Determine the equation of the cubic polynomial graphed below.
From x-intercepts \(-2,1,3\): \((x+2)(x-1)(x-3)=x^3-2x^2-5x+6\). Answer: B
5.
Solve \((x-5)^3+2=-6\).
\((x-5)^3=-8\Rightarrow x-5=-2\Rightarrow x=3\). Answer: D
6.
Determine the degree of the polynomial equation \(y=3x(x+5)^2(x-1)^4\).
Degree \(=1+2+4=7\). Answer: A
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