Solve \( 10 \cdot 3^{x+3}=60 \) to three decimal places. (1 point) -1.369 -2.387 -1.796 -2.169

Use the Remainder Theorem and synthetic division to find each function value. Verify your answers using another method. \( h(x)=x^{3}-5 x^{2}-8 x+4 \) (a) \( h(3)= \) (b) \( h\left(\frac{1}{2}\right)= \) (c) \( h(-2)= \) (d) \( h(-5)= \)

Solve the following simultaneous equations \( x+7 y=10,3 x-2 y=7 \)

Write the function in the form \( f(x)=(x-k) q(x)+r \) for the given value of \( k \). \[ f(x)=x^{3}-4 x^{2}-8 x+14, k=-2 \] \( f(x)=\square \) Demonstrate that \( f(k)=r \). \( f(-2)=\square \)

7. Given \( f(x)=2-\frac{3}{x} \), find \( f^{-1}(x) \) and state its domain and range.

Use synthetic division to show that \( x \) is a solution of the third-degree polynomial equation, and use the result to factor the polynomial completely. List all real solutions of the equation. (Enter your answers as a comma-separated list.) \[ x^{3}+2 x^{2}-3 x-6=0, \quad x=\sqrt{3} \] \( x=\square \)