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Algebra

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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