Kĩ năng phân tích đa thức bậc 2 thành nhân tử #toan7

Lesson 1 so we know that in the second step we multiply 1 by 32 right I take 1 times 3 2 then 3 2 I will analyze it as for example this 1 times 3 2 1 times 3 is 2 or 2 times 16 or is it 4 times 8 Is that right But in this case of 4 times 8 4 plus 8 equals 12 So now I will choose the option to split the number 12 into 4 plus 8 In this way we have a method like this x squared plus 4x Add 8x Add 32 and this one will be x outside x squared plus 4x I put x outside it becomes x times x plus 4 This one I put 8 outside then there is x plus 4 We have a common factor of x plus 4 So we take x plus 4 out Then we will have x plus 4 Multiply by x plus 8 Now I will take 3 multiplied by 3 equals 9 3 multiplied by 3 equals 9 en 9 is separated into 1 and 9 1 multiplied by 9 which is 10 I split into 1 plus 9 that is 1 plus 9 equals 10 So we split it into 10 by 1 plus 9 so we have a profit like this by 3 squared except 1 is also okay except 9 is also okay for example subtract x subtract 9x add 3 this person equals I can factor x ou is 3x-1 except for myself putting 3 outside 3x-1 s is the one I set aside this is x-3 Okay see you this one I'll take 2 times25 2 times 25 Yes fifty right fifty I'll split it into five times ten but if here is a minus sign then now we would consider 10-5 instead of considering 10 -5 please note 10 minus 5 is exactly 5 this one is this one so this number 5 I will split into 10-5 and this is how we will handle it 2 times squared minus 5 becomes 5 equals 10-5 minus 5 equals 5-10 that is we will add 5 Add 5-10 Add 5 to 10 and subtract 10 from it Add 5 except 25 This one I can get out twice right en x-5 multiplied by 2x 2 times plus 5 e x squared xy and y squared terms if you look at it as a degree you see that this is a second-degree equation x is first degree y is first degree but when you multiply two first-degree terms together like x multiplied by x it's the same as multiplying two first-degree terms together which seems to result in x squared at is second level if considered from the first level x is second degree this person is second degree second degree then this is a type called second degree homogeneous form second-degree equatio When encountering this type people do exactly the same as the previous sentences meaning that the fourth sentence will change the way of thinking I do exactly the same for sentence 1 sentence 2 sentence 3 For example I will do it this way Take this number 1 multiply by number 3 1 times 3 equals 3 3 equals 1 times 3 but meanwhile this 1 times 3 equals 4 4 is this number So I will split the number 4 into 1 x 3 I split 4 into 1 x 3 and we will have benefits in this way by x squared xy I split 4 into 1 x 3 and then 4 becomes 1 and 3 3 xy Add 3y squared This person is equal to The greatest common factor of x squared and xy is x right So I factor out x here x multiplied by x and y minus 3y multiplied by x letters y and the common factor will now be x times y multiplied by 3y words Same here 1 x 5 now if I'm here alone and don't care anymore I'll only analyze 5 This number 5 is split into 1 x 5 while 1 x 5 is equal to 6 So this number 6 will be split into 1 x 5 That means we will factor into x times 5xy right and we have a benefit like this by x squared y x y umber 5xy five y squared by Is this x squared and xy correct Here there is a common factor of x so we factor out x Set x outside of x y This places 5y outside then x y becomes x y by placing x y outside then this character is x 5y Similarly I take 2 multiplied by 2 which is4 2 x 2 equals 4 4 I break down into 1 x 4 while the number 5 is being analyzedas 1 x 4 Now this 5xy character I will analyze it into xy and 4xy and then we have an advantage like this by 2 times squared xy character 4xy character plus 2y squared This is the common factor x so we factor x out and it becomes 2x times y I put 2y outside 2y outside then I put 2y here so there's this 2x 2x here is the plus sign this is the plus sign this is the minus sign so this becomes a minus sign minus multiplied by minus gives a plus right Yes this is minus 2y balance and I placed 2y so now there is y here right This is the letter Y and then this person will be 2x the letter y Multiply x by 2y Then continue This person has one actually if you think like that before you would still succeed 9 times 4 is 36 36 is equal to 6 times 6 is 36 while 6 plus 6 is 12 so 12 is when you split it into 6 plus 6 but then we have a different way of thinking that is we will write write this in the form of a list of ideas en becomes 3x all of these squares plus 2 multiplied by 3x multiplied by the number 12 so I split it into 2 x 3 and then multiplied by 2 right We still have 2y left here here2 x 3x x 2y and add to 2y squared This is the correct lifting hook isn't it (3x + 2y) squared This is what we are observing okay It is also 4x all squared minus 2 times 4x which is 8x 5 right Multiply this 5y by this 5y squared this is the first level of the row so this will be equal to what 4 times minus 5y all squared is that correct Here we have a formula for a cubic expansion: (A + B) cubed equals A cubed plus 3A squared B plus 3AB squared plus B cubed A plus B all to the power of 3 is that correct So then this can be seen by the students as such This is 2x all to the power of 3 Plus 3 multiplied by 2x all squared Multiply by 1 right Add 3 times 2x = multiply by 1 squared = 1 cubed plus 1 equals and therefore this one is 2x plus 1 all cubed right Then this will be written as equal to Multiply 2x plus 1 all to the power of 3 This one is different it's a different style it 's meeting a third -year student when we meet a third-year student what do we do What do we do at level 3 in the usual case the usual case I will find x s the solution to the problem is the solution find x is the solution to the problem and this x will be a factor of a factor of the constant term The multiple of the number 6 is 6 12 18 etc What are the multiples of 6 6 plus or minus 1 6 plus or minus 2 Add and subtract 3 Add and subtract 6 so now I will try 1 gold x first 1 gold x I will try putting in s could be 3 minus 6 times 1 squared plus 11 times 1 minus 6 which is 1 minus 6 Add 11 subtract 6 and is this correct or not actually when people check x gold 1 Just do it this way I count the positive number this is a positive number 1 plus 11 is 12 you know then count the negative number 6 plus 6 is 12 so so they are both 12 meaning they are equal then it means x plus 1 will be a solution When x equals 1 is a root then there will be a factor of x minus 1 right So I will factor this one eo nhân tử x-1 và do đó bạn này sẽ được phân tích như thế này x-3 trừ x-bình tại sao lại là trừ x-bình Because when I put x-bình outside it will appear as x-1 like this right Then now it is minus 6 But I only subtracted 1 right so subtract 1 how much more to subtract then you can subtract 6 here I subtracted x minus 2 but this is minus 6 average points so there must be a way of thinking that minus 1 minus how much more equals minus 6 The answer is minus 5 so we will minus 5 here minus 5 x-square right en 5 x-bình this must be combined with how many x to later have a factor of x-1 then it would be I have to add 5 times zero Because later I will put 5 times outside it will appear as x-1 like this right So I will have to add 5x here we add 5x here en now look around please this is 11 and this is plus 5 the children know that 5 plus how muc o make 11 how much is it 6 right plus 6 5 x 6 is 11 so here we will plus 6 x here and finally the number minus 6 we put here put minus 6 times 6 here it's perfect minus 6 that 's this perso en I put the x outside Put x outside then there is x-1 This person has 5 shared I placed 5 outside en still x-1 This is number 6 in the middle I placed 6 outside and will become x-1 multiplied by x squared minus 5x plus 6 This is step 2 of the demonstration right I will do the same as the previous sentences 1 2 3 and that will give the result x-1 multiplied by x -2 multiplied by x-3 just now I'm done the trigonometric equations right now to the minimum value problem find the minimum value saying it like this means You can find the minimum find the minimum you can find the cheapest find the cheapest but the main skill is to create products The main skill It creates a row of equations Then now let's start with question A right Is it x squared plus x y squared plus 2i Hey you What is this x times y all squared plus 2 multiplied by x times y this plus 2 right Here you see this here you see is it a meal okay by the square of y all squared Add 2 multiply by x you y Add 2 x is the same as y is x y is the friend x y is all squared and there is 2 press x plus y then put 2 outside This is it I left number 2 here Then you remember that a squared plus 2a equals if you add 1 more then this is (a + 1) squared right So this structure I will separate the number 2 from 1 plus 1 like this and this phrase becomes this equation Is x plus y plus 1 squared There that 's why we have this one equals to that (x + y + 1) squared and even if it spreads out 1 like this then obviously this is equal to 1 the minimum value is 1 Is the wind equal to x plus y equals 1 Four x squared is equal to two x all squared right Plus 2 times 2x times y plus y squared This is the formula 2x plus y all squared Actually those who have experience This is the formula and it is 2x plus y all squared Right So we will have it transformed like this by 2x plus y all squared minus Here there are 4 and 2 of these I can take 2 out here Then there is 2x plus y Does that make ten What is this person's level This if we imagine as 2x plus y equals a then this is a squared it is in the form of a squared plus Minus 2a plus 10 right a squared minus 2a plus 1 will result in the identity of du da 9 So it's a minus 1 equals all squared plus 9 Is that right So we will have this analysis: 2x plus y except 1 x squared plus 9 This one x squared plus y squared but there's no xy right There's no 2y right Then we can connect like this: x squared plus 4x plus 4 becomes x plus 2 squared Similarly y squared minus 4y plus 4 will become y minus 2 squared So this one I will analyze it by x plus 2 all squared plus y minus 2 all squared X squared plus 4x I have to add 4 as well y squared minus 4y I have to add 4 as well So I have already added 8 This is number 12 which has 8 plus 4 more Therefore there is still 4 more Add 4 and it is equal to 4 The minimum value of c is 4 Hiding the equation gives x equals 2 and y equals 2 Question 14 This question has x squared here so I do the division action dividing each one down dividing down and dividing down Then your d will be equal to 1 divided by x minus 8 on x Add 4 I take 1 divided by x squared here which gives 1 over x squared 8x over x squared here which will give 8 over x 4x squared On the road it turns out to be 4 This looks simple this is 1 over x minus 4 all squared right If 1 over x is called A then it has the form A squared minus 8A plus 4 plus 4 then here I am I analyze it as A squared minus 2A times 4 plus 16 then you have to subtract 12 Then it will become A minus 4 squared Therefore here it will become 1 over x minus 4 squared minus 12 here Is that right This problem is when you multiply into 3x minus x squared plus 5y minus y squared right Then the minus sign of the squared x with the minus y squared I have an action which is to subtract 1 from the place E Then E minus E E equals x squared minus 3x square plus y squared minus 5y Then use the standard techniques For example x squared minus 2x times 3 over 2 Number 3 is split into 2 and 3 halves not 9 quarters Then we have to add 9 quarters then 9 quarters minus 9 and 4 parts And become x minus 3 over 2 squared minus 9 over 4 Completely similar to this I will get that this will be equal to x minus three halves all squared plus this will be 2 times 5 halves then I have to add 25 quarters then I have to subtract 25 quarters Then what is this this is x y minus 5 over 2 all squared minus 25 over 4 Minus 5 and a half All squares and subtracted by and so just now it was subtracted by 9 over 4 and now subtracted by 25 over 4 Is it minus 34 parts 4 no 34 divided by 4 is 17 divided by 2 So I subtract 17 divided by 2 Then except E This is equal to minus 17 over 2 So minus E is equal to minus 17 over 2 Is that right So you know the rule of changing signs right For example the rule of changing signs is minus A equals minus B so we remove the minus sign Then I turned back to the shore of awareness Then Thus we obtain our own E It will turn bac less than or equal to 17 parts 2 The teacher has finished treating him here 15 sentences Then the main skill to factor is for quadratic equations which is to multiply A by C This is B Multiply A B C Then separate the product Multiply into two numbers that when multiplied together equal B This is the main skill of the problem 1 2 3 are the same article 4 5 6 are the same 4 5 6 are the same article 7 article 8 lesson 7 8 9 are the same using the same formula lesson 10 is analyzing how to factor a cubic polynomial The problem of min is a mathematical problem The key skill is to create a product This sentence must be created before the product is made Make it nea Then create the dis Let's stop here