Phân tích đa thức thành nhân tử = phương pháp đổi biến:
a) \(\left(x^2+x\right)-2\left(x^2+x\right)-15\)
b) \(x^2+2xy+y^2-x-y-12\)
c) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\)
d) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
e) \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4\)
2 Tìm giá trị nhỏ nhất của biểu thức :
a) A=2x^2-8x+10 ; b) B= x(x+1)(x^2+x-4)
d) D=9x^2-6x+5 ; e) E=x^2+3-1
f) F=(x^2+5x+4)(x+2)(x+3) ; G= (x-3)(x-4)(x^2-7x+8)
h) H=\(\left|x-7\right|+\left|x+5\right|\) ; i) I=\((2x-1)^2-3\left|2x-1\right|+2\)
k) K=\(\left|x^2+x+1\right|+\left|x^2+x-12\right|\)
Bài 2: Giải các phương trình sau:
a \(\frac{3x+2}{2}-\frac{3x+1}{6}=\frac{5}{3}+2x\)
b \(\left(x+1\right)\left(x+2\right)=\left(2-x\right)\left(x+2\right)\)
c \(\frac{x+5}{x-5}-\frac{x-5}{x+5}=\frac{20}{x^2-25}\)
d\(x^2+6x+9=114\)
3x\(\left(x-a\right)+5a\left(a-x\right)\)
Tìm tất cả các số nguyên n để:
a) \(\left(2n^2+n-7\right)\) ⋮\(\left(n-2\right)\)
b) \(\left(10n^2+n-10\right)\) ⋮\(\left(n-1\right)\)
c) \(\left(3n^3+10n^2-5\right)\) ⋮\(\left(3n+1\right)\)
d) \(\left(n^3-3n^2-3n-1\right)\)⋮\(\left(n^2+n+1\right)\)
Phân tích các đa thức sau thành nhân tử:
a) \(4x^4-32x^2+1\)
b) \(x^6+27\)
c) \(\left(2x^2-4\right)^2+9\)
d) \(4x^4+1\)
e) \(4x^4+y^4\)
f) \(x^4+324\)
Rút gọn
a) \(\sqrt{5}.\sqrt{45}-\sqrt{13}.\sqrt{52}\)
b) \(\sqrt{2300}.\sqrt{23}+\frac{\sqrt{6}}{\sqrt{150}}+\sqrt{\frac{25}{144}}\)
c) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)
d) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)
e) \(\left(4+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)
1. There/two/armchairs/left corner/living-room
2. Next to/my house/large park
3. Right side/room/there/door
4. there/T.V set/beside/bookshelf
Exercise 1. Choose the right answers.
1. My father's death left me with a great ....................... in my heart.
A. empty B. emptiness C. emptying
2. It was a really ................... experience. Everybody was very .................
A. terrifying/shocking
B. terrified/shocking
C. terrifying/shocked
3. There was a ................. change in the weather.
A. sudden B. suddenness C. suddenly
4. “How did you learn to drive?” “My father..................... me.”
A. taught B. has taught C. teaches
5. The teacher's explanation was .............. . Most of the students didn't understand it.
A. confusion B. confusing C. confused
6. If you make a good ................... at the interview, you will get the job.
A. impression B. impressive C. impressed
7. I've been working very hard all day and now I'm ..........................
A. exhausting B. exhausted C. exhaustion
8. If you stop by the ............., please buy me a loaf of bread.
A. bakery B. baking C. bake
9. Everybody at the carnival was .................... dressed.
A. colourful B. colourfully C. coloured
10. Linda usually wears ..................... clothes.
A. colourful B. colourfully C. coloured
11. Hello! I've just...................to the shops. I've bought lots of things.
A. been B. gone C. went
12. Why do you always look so ................? Is your life really so ................... ?
A. boring/ bored B. bored/ boring C. bored/ boring
13. Americans fought hard to earn their ....................... from Britain.
A. free B. freely C. freedom
14. Sam ............................ (take) a picture of me while I ..................... (not/look).
A. took/was not looking
B. has taken/was not looking
C. took/didn’t look
15. “Where are you going for your holiday?” “I ......................... yet.” (not/decide)
A. didn’t decide B. haven’t decided C. don’t decide
16. Sue works........................ She never seems to stop.
A. continuously B. continue C. continuous
17. Fill in your name, address and ..................... on the form.
A. nation B. nationality C. national
18. He's one of the most ................... people I've ever met. He never stops talking and he
never says anything .........................
A. boring/ interesting
B. bored/ interesting
C. boring/ interested
19. Rachel and Patrick are very ................ married.
A. happy B. happiness C. happily
20. “Are you going to the bank?” “No, I've already...............to the bank.”
A. gone B. go C. been
Exercise 2. Put a/an, the or 0 (zero article) in the spaces.
1. A special award was given to ....................... novelist Ian McMurphy.
2. I’ve been offered the position of .................... Director of Personnel.
3. I’ve always wanted to meet ..................... Michael Owen.
4. What's ................ name of that man we met yesterday?
5. I’m ...................... marketing adviser at Unifleet.
6. Let me introduce you to ........... Paula Cox.
7. We meet our good friend ......... Jean when we were in ......... New York City.
8. Brian’s ............. manager of the local football team.
9. When she was young she knew ................ Picasso.
10. She was determined to be ............ author.
11. We’re going on holiday with .................. Smiths.
12. He’s really keen on playing football. He likes to think of himself as
.............. Ronaldo.
13. We had dinner in ................. very nice restaurant.
14. This morning I bought ........... newspaper and ........... magazine. ............
newspaper is in my bag, but I can’t remember where I put ............ magazine.
15. My friends live in ........ old house in small village. There is .............
beautiful garden behind house. I would like to have ............. garden like that.
Exercise 3. Rewrite the senctences without changing their meaning.
1. She started driving a year ago.
→ She has ...................................................................................................
2. We began eating when it started to rain.
→ We have .....................................................................................................
3. I have never been to France before.
→ This is .........................................................................................................
4. I last had my hair cut 2 weeks ago.
→ I haven’t ......................................................................................................
5. I began living in Ho Chi Minh city when I was 8.
→ I have ...........................................................................................................
6. I haven’t seen him for a month.
→ The last time ................................................................................................
7. She has moved to Paris for 3 years.
→ She moved ..................................................................................................
8. I started learning English 5 years ago.
→ I have ...........................................................................................................
9. He has not written to me since April.
→ The last time ................................................................................................
10. The last time she saw her elder sister was in 2006.
→ She hasn’t ...................................................................................................
11. I haven’t slept since 2 days ago.
→ I last ............................................................................................................
12. We haven’t met since 2019.
→ The last time ................................................................................................
13. I have worked for this company for 6 years.
→ I ....................................................................................................................
14. I last saw him at work yestersday.
→ I haven’t .......................................................................................................
15. Alex and Elizabeth married ten years ago.
→ Alex and Elizabeth ......................................................................................
1.You/shouldn'/point/prong/fork/upwards/during/meal.
2.You/can/use/fork/pick/more/food/dish.
3. The knife/hold/right/hand/and/fork/hold/left/hand.
4.When/meal/finish//you/should/put/knife and fork/plate.
5.Same/cutlery/apply/eat/main/course/and/dessert.