4. Une con una línea cada polinomio con su respectiva factorización. \[ \begin{array}{ll}\text { a. } x y-4 x+y-4 & (a+1)(x-2 y) \\ \text { b. } a(n+2)+(n+2) & (x+1)(y-4) \\ \text { c. }-5 x(a+c)+2 y(a+c) & (2-3 z)(3 x-2 y) \\ \text { d. } 6 x-4 y+6 y z-9 x z & (n+2)(a+1) \\ \text { e. } x(a+1)-2 y(a+1) & (a+c)(2 y-5 x)\end{array} \]

\( x=3f(x)=\frac{1}{2}x^{2}-\frac{1}{2} \)

Perform the indicated operations, then simplify. \( \frac{5 y}{y+6}+\frac{7 y^{2}}{y^{2}-36}-\frac{4}{y-6} \) \( \frac{7 y^{2}+5 y-4}{y^{2}+2 y-36} \) \( \frac{12 y^{2}-34 y-24}{(y+6)(y-6)} \) \( \frac{12 y^{2}-34 y+24}{(y-6)(y+6)} \) \( \frac{7 y^{2}+5 y-4}{(y+6)(y-6)} \)

b. read none of magazine at all c. read exactly one of the magazines. 3. Use Mathematical induction to prove that \( x^{n}+y^{n} \) is divisible by \( x+y \) for odd natural number \( n \geq 1 \). 4. Solve the equation \( z^{6}+1=\sqrt{3} i \) where \( z \in c \).

2. Find the value of \( x \) if \( 9^{x+1}=27 \)

Add. State the sum in simplest form. \( \frac{a^{2}-6}{15 a^{3} b^{2}}+\frac{3}{10 a b^{2}} \) \( 0 \frac{a^{2}-3}{150 a^{4} b^{4}} \) \( \frac{a^{2}-3}{15 a^{3} b^{2}+10 a b^{2}} \) \( 0 \frac{a^{2}-3}{30 a^{3} b^{2}} \) \( \frac{11 a^{2}-12}{30 a^{3} b^{2}} \)