To decompose a polynomial into factors, the general procedure is to first -- and then -- when each term of the polynomial has a common factor————

To decompose a polynomial into factors, the general procedure is to first -- and then -- when each term of the polynomial has a common factor————

Extracting common factors and merging similar items
If the square of the equation x-3 / X-1 = 3x-9 / k about X has an increasing root, then K=
The solution equation: (x-1) (3x-9) = K & # 178; (x-3) = > 3x-3 = K & # 178; (x ≠ 3) = > x = K & # 178; (3 + 1)
∵ x = 3 is the increasing root ∵ K & # 178; = 3 + 1 = 3 = > k & # 178; = 6 = > k = ± √ 6
Follow up questions
Two cars start from place a at the same time and drive along a highway to place B. car a travels 8 kilometers more per hour than car B. car a arrives at place C 40 minutes earlier than car B. when car B arrives at place C, car a just arrives at place B. It is known that the distance from place C to place B is 40 kilometers
How many kilometers per hour does car B travel?
In this case, a arrives at C 40 minutes earlier than B. that is to say, after a arrives at C, B also arrives at C 40 minutes later. When B arrives at C, a just reaches B. so it takes a total of 40 minutes for a to drive from C to B. so the speed of a is 60 km / h. When a arrives at B, B just reaches C, which means that in this process, a is faster than
Let a arrive at C40 minutes earlier than B, that is to say, when B arrives at C, a walks for another 40 minutes (2 / 3 hours), and then a arrives at B, so 40 = 2x / 3; so x = 60, y = 52; if B arrives at C, a will walk for another 40 minutes (2 / 3 hours);
The answer is that B travels 52km per hour;
A: let car B travel x km per hour
（ x+8）*40/60=40
x+8=60 x=52
Suppose that the speed of car B is x, then the speed of car a is (x + 8). Suppose the distance between AB is s, then the distance between AC is (S-40)
According to the following equation:
(S-40) / (x + 8) = [(S-40) / x] - 40
(S-40)/X=S/(X+8)
The solution of linear equations of two variables is obtained
In factorization, if the coefficients are fractions, how to choose the coefficients of the common factor?
Example: what is the common factor of 1 / 3 N plus 1 power plus 1 / 6 N plus 1 / 9 n minus 1 power?
It's not good to use 1 / 3, is it 1 / 18 or 1 / 9?
This problem ~ extract anything can ~ key to see how you use in the problem
This problem extracts 1 / 3 of N plus 1 power ~ 1 / 3 of n power ~ 1 / 3 of n minus 1 power~
All right~
If you want to extract the common factor ~ extract the N + 1 power of 1 / 18~
wish you success!
If the equation x + 1-3x / 1 = 3x-3x / 3 x + k of X has an increasing root, find the value of increasing heel and K
In this way, it's hard to guarantee that you don't misunderstand the meaning of the question. Can't you write the question clearly?
Answers to the practical questions of quadratic equation with two variables
Transportation company a decided to transport 10 tons of apples to city a and 8 tons to city B respectively, but now there are only 12 tons of apples, and 6 tons still need to be transported from transportation company B. after negotiation, the transportation costs of 1 ton of apples from transportation company a to city a and B are 50 yuan and 30 yuan respectively, and the transportation costs of 1 ton of apples from transportation company B to city AB are 80 yuan and 40 yuan respectively. The total transportation costs are 840 yuan. How to carry out the transportation?
Suppose that x tons of apples are transported to city a and Y tons to city B from transportation company A
The transportation company B needs to transport 10-x tons of apples to city a and 8-y tons to city B
x+y=12 ①
50x+30y+80(10-x)+40(8-y)=840 ②
The solution is x = 8, y = 4
It is necessary to transport 8 tons of apples from transportation company a to city a and 4 tons to city B
Transport 2 tons of apples from B transportation company to a city and 4 tons to B city
Let's transport x tons of apples from company a to city a and Y tons of apples from company B to city A
x + y = 10
50x + 80y + 30(12-x) + 40(6-y) = 840
Just solve the equations
Suppose that a transports x tons of apples to a and B transports y tons of apples to a, then a transports 12-x tons to B and B transports 6-y tons to B
Countable equations: x + y = 10
50x+80y+30(12-x)+40(6-y)=840
The solution is: x = 8, y = 2
That is, 8 tons of apples will be transported from company a to city a and 4 tons to city B,
From B city to Apple company, 4 tons
Good style, good ventilation
What about factorization with fractions? For example - 1 / 2x ^ 3 + 2XY XZ factorization, what is the common factor
-1/2x^3+2xy-xz
=(-1/2)x(x²-4y+2z)
Bring up the score
The equation is solved by the method of flattening: 4 (2x-5) &# 178; = 9 (5 + x) &# 178;
(until 21 o'clock tonight)
The solution is 4 (2x-5) &# 178; = 9 (5 + x) &# 178;
Get [2 (2x-5)] ^ 2 = [3 (5 + x)] ^ 2
That is, (4x-10) ^ 2 = (15 + 3x) ^ 2
That is, 4x-10 = 15 + 3x or 4x-10 = - (15 + 3x)
That is, x = 25 or 7x = - 5
That is, x = 25 or x = - 5 / 7
A binary linear equation application problem~
There are 90 workers in the workshop, each of whom processes 15 shafts or 12 sets of bearings on average every day. How many workers should be allocated to process shafts and how many people should process bearings so that shafts and bearings can be matched?
Set X name to process shaft and Y name to process bearing
X+Y=90
15X=12Y
The solution is as follows
X=40
Y=50
If x people produce shaft rod, 90-x people produce bearing
15X=12*(90-X)
15X=1080-12X
27X=1080
X=40
90-40=50
40 workers should be assigned to process the shaft rod and 50 workers to process the bearing, so that the shaft rod and the bearing can be matched
How to extract the common factor and how to calculate it?
Power 8a3, power B2 + power 12a, power B3
8a^3·b^2 + 12a·b^3 = 4a·b^2·(2a^2 + 3b)