9. The dentist pulled out my tooth.

→ My tooth __________was pulled out ____________________by the dentist.

10. The police are questioning him now.

→ He _______is being questioned_______________________ now by the police

11. The waitress serves breakfast at 7 o’clock.

→ Breakfast ____is served at 7 o' clock__________________________ at 7 o’clock by the waitress.

12. Who did they give the prize to?

→ Who ____was___the prize______given_______________ to ?

13. The news seemed to have shocked him.

→ He seemed ________to be have been shocked______________________by the news.

14. You should take these tablets before meals.

→ These tablets _____should be taken_________________________ before meals.

15. The teacher has sent him out of the classroom.

→ He _________has been sent_____________________out of the classroom by the teacher.

16. You must wash coloured clothes separately.

→ Coloured clothes _________must be washed_____________________separately.

17. The mayor will open the new sports center next month.

→ The new sports center ______will be opened________________________by the mayor next month.

18. Many parents influence their children strongly.

→ Children __________are influenced____________________ strongly by most parents.

19. They were pulling down the building when I walked by.

→ The building _______was being pulled_______________________down when I walked by.

20. Somebody has stolen Jack's car recently.

→ Jack’s car _________has been stolen_____________________ recently.

21. He expects people to show him more respect.

→ He expects _________to be showed_____________________more respect.

22. Nobody has seen the Queen since July.

→ The Queen _______hasn't been seen_______________________ since July.

\(A=\dfrac{2x+1}{x-8}\)

\(A=\dfrac{2x-16+17}{x-8}\)

\(A=2+\dfrac{17}{x-8}\)

A nguyên \(\Leftrightarrow\dfrac{17}{x-8}\) nguyên

\(\Leftrightarrow x-8\in\text{Ư}\left(17\right)=\left\{\pm1;\pm17\right\}\)

+) x - 8 = 1 <=> x = 9

+) x - 8 = -1 <=> x = 7

+) x - 8 = 17 <=> x = 25

+) x - 8 = -17 <=> x = -9

\(A=\dfrac{2x+2}{x-8}=\dfrac{2x-16+18}{x-8}=\dfrac{2\left(x-8\right)+18}{x-8}=2+\dfrac{18}{x-8}\)

Để A nguyên

\(\Leftrightarrow\dfrac{18}{x-8}\) nguyên

<=> x - 8 thuộc Ư(18) = \(\left\{\pm1;\pm2;\pm3;\pm6;\pm9;\pm18\right\}\)

Bảng tìm x 

Vậy .........................

\(A=\dfrac{2\left(x-8\right)+17}{x-8}=2+\dfrac{17}{x-8}\Rightarrow x-8\inƯ\left(17\right)=\left\{\pm1;\pm17\right\}\)

\(x^5+x^4+1\)

\(=x^3\left(x^2+x+1\right)-x\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^3-x+1\right)\left(x^2+x+1\right)\)

\(x^8+x+1\)

\(=x^6\left(x^2+x+1\right)-x^5\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)

\(=\left(x^6-x^5+x^3-x^2+1\right)\left(x^2+x+1\right)\)

\(B=1...12...25\) (\(2014\) chữ số \(1\), \(2015\) chữ số 2)

\(=5+2\left(10+10^2+...+10^{2015}\right)+\left(10^{2016}+10^{2017}+...+10^{4029}\right)\)

\(=5+2.10\left(1+10+...+10^{2014}\right)+10^{2016}\left(1+10+...+10^{2013}\right)\)

\(=5+2.10.\dfrac{10^{2015}-1}{9}+10^{2016}.\dfrac{10^{2014}-1}{9}\)

\(=\dfrac{45}{9}+\dfrac{2.10^{2016}-20}{9}+\dfrac{10^{4030}-10^{2016}}{9}\)

\(=\dfrac{\left(10^{2015}\right)^2+10.10^{2015}+25}{9}\)

\(=\left(\dfrac{10^{2015}+5}{3}\right)^2\)

- Vì \(\left\{{}\begin{matrix}10^{2015}mod3=1\\5mod3=2\end{matrix}\right.\Rightarrow\left(10^{2015}+5\right)⋮3\)

\(\Rightarrow\dfrac{10^{2015}+5}{3}\) là số tự nhiên.

Vậy B là số chính phương.