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# SAT Polynomials

If $$x\neq \pm3$$ and $$m=\frac{x^2-5x-24}{x^2- 9}$$, which of the following is equivalent to $$m$$?

(A) $$\ \ \frac{x-24}{x-9}$$

(B) $$\ \ \frac{x-8}{x-3}$$

(C) $$\ \ \frac{x+8}{x-3}$$

(D) $$\ \ \frac{x-8}{x+3}$$

(E) $$\ \ \frac{(x-8)(x-3)}{(x+3)^{2}}$$

If $$hk=2$$, which of the following is equivalent to $$hkx^{3}+7hkx^2-7hk$$?

(A) $$\ \ 2(x^{5}-7)$$
(B) $$\ \ 2(x^{3}+7x^{2})$$
(C) $$\ \ 2(x^{3}-7)^{2}$$
(D) $$\ \ 2(x^{3}+7x-7)$$
(E) $$\ \ 2(x^{3}+7x^{2}-7)$$

If $$x=k(k-4)(k+4)$$, which of the following equals $$x+1$$?

(A) $$\ \ 3k$$
(B) $$\ \ k^{2}-16$$
(C) $$\ \ k^{3}-17$$
(D) $$\ \ k^{3}-16k$$
(E) $$\ \ k^{3}-16k+1$$

If $$x^{2}+y^{2}=324$$ and $$(x-y)^{2} =16$$, what is the value of $$xy$$?

(A) $$\ \ -170$$
(B) $$\ \ -154$$
(C) $$\ \ -14$$
(D) $$\ \ 154$$
(E) $$\ \ 308$$

Let $$x$$ and $$y$$ be two positive consecutive even integers, such that $$y>x$$. Of the following, which is equal to $$y^{2}-x^{2}$$?

(A) $$\ \ -4x+4$$
(B) $$\ \ 2x+1$$
(C) $$\ \ 2x+4$$
(D) $$\ \ 4x+4$$
(E) $$\ \ x^{2}+4x+4$$

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