Answer all the questions. Show your work
1) Factor the expression by removing the common factor with the smaller exponent.
$2x(x-5)^3 - 4x^2(x-5)$
2) Simplify the expression:
$\frac{1}{\sqrt{x+h+2}-\sqrt{x+2}}
$
3) Simplify the difference quotient by rationalizing the numerator
$\frac{\sqrt{x+3}-\sqrt{3}}{h}$
$\frac{\sqrt{x+h-2}-\sqrt{x-2}}{h}$
a)
b)
4) if $f(x) = x^2 - x + 1$, find
5) Evaluate the indicated function for $f(x) = x^2 + 5$, and $g(x) = x - 3$
a) $(f \circ g)(1)$
b) $(f + g)(t - 2)$
c) $(f/g)(0)$
6) Solve the inequality: $x^2 + 2x > 3$
7) Solve the inequality: $x^2 < 25$
8) Solve the inequality: $\frac{5}{x-6} > \frac{3}{x+2}$
9) Solve the system of equations
$x + 11y = 4$,
$2x^2 - 5y = 9$
10) Write the partial fraction decomposition of the rational expression.
a) $\frac{1}{4x^2 - 9}$
b) $\frac{x+1}{x^2+x}$
c) $\frac{x+2}{x(x-4)}$
11. Solve by using the Cramer Rule
$3x + 2y = 27$
$4x - 4y = 26$
