Use the Factor Theorem to determine whether \( x-2 \) is a factor of \( P(x)=x^{3}-3 x^{2}-4 x+ \) Specifically, evaluate \( P \) at the proper value, and then determine whether \( x-2 \) is a factor. \( \begin{array}{l}P(\square)=\square \\ x-2 \text { is a factor of } P(x) \\ x-2 \text { is not a factor of } P(x)\end{array} \)

A. \( 4 x^{2} y\left(x z^{2}+5 w x y+3\right) \).

Solve the equation by factoring. \[ x^{2}=7 x-12 \]

4) Dado el dominio de cada función, determina el recorrido. \( \begin{array}{ll}\text { a. } f(x)=20 x \text { y } \operatorname{Dom}(f)=\{0,1,2,3\} & \text { b. } g(x)=-5 x \text { y } \operatorname{Dom}(g)=\{0,3,6,9\} \\ \text { c. } h(x)=x-3 \text { y } \operatorname{Dom}(h)=\{-2,-1,0,1\} & \text { d. } j(x)=3 x+4 \text { y } \operatorname{Dom}(j)=\{0,5,10,15\}\end{array} \)

5) Sea una función lineal cuya gráfica pasa por los puntos \( (6,3) \) y \( (-2,-1) \). a) Determine la función b) ¿Cuál es el valor de \( f(-3) \) y de \( f(8) \) ? c) ¿Es creciente o decreciente?

Solve the following equations and inequalities analytically. Support your solutions graphically. \( \begin{array}{lll}\begin{array}{ll}\text { (a) }|2 x+1|+3=5 & \text { (b) }|2 x+1|+3 \leq 5 \\ \text { (c) }|2 x+1|+3 \geq 5\end{array} \\ \text { A. The solution set is the finite set of real numbers }\{ \\ \text { (a) Find the solution for }|2 x+1|+3=5 \text {. Select the correct choice below, and fill in the } \\ \text { answer box if necessary. } \\ \text { expression. Use a comma to separate answers as needed.) } \\ \text { B. The solution set is the interval } \square \text {. } \\ \text { (Type your answer in interval notation. Use integers or fractions for any } \\ \text { numbers in the expression.) } \\ \text { C. The solution set is } \varnothing \text {. }\end{array} \).