1. x-intercepts: $3\pm \sqrt{7}$

2.

3. (1, 10)

4. $(-\infty ,-4)\cup (-4,1)\cup (1,\infty )$

5. Quotient:$x^2-4x+3;$ remainder: 0

6.

7. $-2,1,2$

8. Quotient: $-3x^2+5x+1$

9. $P(-2)=-53$

10. $-2,2,5$

11. $0,-{\displaystyle \frac{1}{2}}+{\displaystyle \frac{\sqrt{61}}{2}},-{\displaystyle \frac{1}{2}}-{\displaystyle \frac{\sqrt{61}}{2}}$

12. $-9,-{\displaystyle \frac{9}{2}},-3,-{\displaystyle \frac{3}{2}},-1,-{\displaystyle \frac{1}{2}},{\displaystyle \frac{1}{2}},1,{\displaystyle \frac{3}{2}},3,{\displaystyle \frac{9}{2}},9$

13. $f(x)\to -\infty$ as $x\to -\infty$ and $f(x)\to \infty$ as $x\to \infty$

14. $x=-2,$ multiplicity: 3; $x=2,$ multiplicity: 1

15. Number of positive zeros: 0 or 2; number of negative zeros: 1

16. Horizontal asymptote: $y=2;$ vertical asymptotes: $x=-4$ and $x=5$

17. $y={\displaystyle \frac{kx}{t^2}},$ where $k\ne 0$ is a constant

18. $y=4$

19. $x=15$

20. $V(x)=x(8-2x)(17-2x)$