Decompose the following factors: (1)-6x²+12x+6 (2)x²-xy+x (3)9x³-21x³y²+12x²y²

Decompose the following factors: (1)-6x²+12x+6 (2)x²-xy+x (3)9x³-21x³y²+12x²y²

One
6（-x²+x+6）
Two
x(x-y+1)
Three
3x²(3x-7x*y²+4y²)
1.-6(x^2-2x-1)
2.x(x-y+1)
3.3x^2(3x-7xy^2+4y^2)
Remember, it's a one variable equation! Two variables or anything else, no!
A pile of fruit is packed in two bags, one half of which is taken from bag a and 12 kg from bag B, then the weight of the remaining fruit in the two bags is equal. At this time, if another half is taken from the remaining fruit in bag B, then one third of the original weight of bag B is left in bag B. how many kg is the total weight of the pile of water fruit?
If bag B contains x kg of fruit, bag a contains 2 (X-12) kg of fruit
(x-12)/2 = x/3
The solution is 3x-36 = 2x
X = 36
So there are fruits in the bag 2 (X-12) = 48 (kg)
This pile of fruit weighs 36 + 48 = 84 (kg)
The fruit in bag B is XKG
∴0.5（x-12）=1/3x
The solution is x = 36
2 * (36-12) = 48kg
A total of 48 + 36 = 84kg why? ∵ originally, 12 kg of XKG was taken as X-12, and another half of the remaining fruit in bag B was taken as 0.5 (X-12)
One third of the original weight of bag B is left in bag B
∴0.5（x-12）=1/3x
Take half from bag a and 12 kg from bag B
The fruit in bag B is XKG
∴0.5（x-12）=1/3x
The solution is x = 36
2 * (36-12) = 48kg
A total of 48 + 36 = 84kg?
If the left side of the equation 4x2 - (m-2) x + 1 = 0 is a complete square, then the value of M is______ .
∵ 4x2 - (m-2) x + 1 = (2x) 2 - (m-2) x + 12, ∵ (m-2) x = ± 2 × 2x × 1, ∵ m-2 = 4, or m-2 = - 4, the solution is m = 6 or M = - 2
Using equation solution and arithmetic solution, Xiao Ming measured the circumference of the trunk of a tree with the same rope. He circled it with two fold rope for more than 1.5 meters, and circled it with three fold rope for more than 2 meters
The length of the rope is 2 * 2 = 4 times more than 1.5 * 2 = 3 meters of the girth of the tree after two turns of the rope. The length of the rope is 1 * 3 = 3 times more than 2 * 3 = 6 meters of the girth of the tree after two turns of the rope. The girth of the tree trunk is x meters. 2x × 2 + 2 × 1.5 = 3x + 3 × 2x = 3
It is known that the left side of the equation 4x ^ 2-4x + n = 1-m is a complete square, and the equation about X has a real number solution
Finding the solution set of the inequality my + Mn > y + n about y
The equation 4x ^ 2-4x + n = (2x) ^ 2-4x + n = (2x-1) ^ 2 + n-1 is a complete square
Then n-1 = 0 and N = 1
The equation about X has a real solution, so 1-m ≥ 0, that is, m ≤ 1
My + Mn > y + N, that is, (m-1) y > 1-m,
When m = 1, there is no solution,
When m
4x²-4x+1-1+n=1-m
(2x-1) & sup2; - 1 + n is the square form, then - 1 + n = 0
N=1
4X & sup2; + 4x + N + M-1 = 0 has real solution
So 16-16 (n + m-1) > = 0
n+m-1
Use the equation to solve the problem. If you don't use the equation, use the arithmetic method to explain the detailed process ideas,
A batch of yellow sand is transported by 5 trucks in the morning and the same 8 trucks in the afternoon. As a result, 40.5 tons of yellow sand is transported less in the morning than in the afternoon. How many tons of yellow sand are transported by each truck?
Each truck carries x tons,
A series of equations,
5x＋40.5＝8x
The solution is x = 13.5 (tons)
If you use arithmetic,
8 in the afternoon, 5 in the morning, 8-5 = 3 in the morning
Less than 3 vehicles, less than 40.5 tons, each vehicle: 40.5 △ 3 = 13.5 (tons)
The left side of equation 4-8x + 4x & # 178; = 9 is____ This equation can be reduced to_____ =After 9, the number of times was reduced_____ The root of the equation is x1___ ,x2___
The left side of equation 4-8x + 4x & # 178; = 9 is_ Perfect square___ This equation can be reduced to 4 (x-1) ² = 9 and then reduced to degree_ 2（x-1)=3 2(x-1)=-3____ The root of the equation is X1 = - 1 / 2___ ,x2_ =5/2__
The left side of the equation 4-8x + 4x & # 178; = 9 is the (standard) form. The equation can be reduced to 4 (x-1) &# 178; = 9 and then reduced to degree. The roots of the equations (2 (x-1) = 9 and 2 (x-1) = - 9) are X1 = (13 / 4) x2 = (- 5 / 4)
Polynomial 4 (x-1) &# 178; 2 (x-1) = - + 3 1 / 2 5 / 2
The left side of equation 4-8x + 4x & # 178; = 9 is in the form of complete square difference. This equation can be reduced to (2x-2) &# 178; = 9 and then reduced to 2x-2 = ± 3. The root of the equation is X1 = - 1 / 2, X2 = 5 / 2
Complete square, (2-2x) & #, 2-2x = ± 3, = 5 / 2, = - 1 / 2
A mathematical problem. Arithmetic equation can, do not binary first power equation. 3Q
The existing fresh orange juice water with 40% juice content is 500g. How many g juice should be added to turn it into fresh orange juice water with 60% juice content?
The existing fresh orange juice water with 40% juice content is 500g. How many g juice should be added to turn it into fresh orange juice water with 60% juice content?
Suppose you need to add XG juice
40% fresh orange juice, containing 0.4 * 500 juice. When fresh juice is added, the content of juice becomes 0.6 * (500 + x)
When the difference between them is XG, the following equation can be obtained
0.4*500+x=0.6*(x+500)
0.4x=0.2*500
x=250
Add 250g juice
(40%×500+X) /(500+X) =60%
X=250
Add 250g juice
Add x grams of juice
（500×40%+x）=60%×（500+x）
The solution is: x = 250 G
Let XG be added
According to the known calculation, it contains 200 grams of orange juice
So 200 x / 500 x = 60%
The solution is x = 250
Let's add x grams of juice,
（500*40%+X）/（500+X）=60%
200+X = 300+0.6X
0.4X=100
X=250（g）
A: add 250g juice.
The left side of the equation is reduced to the product of two univariate factors (1) x & # 178; - 4x-21 = 0 (2) x & # 178; - 2x-8 = 0
（1）（x+3）（x-7）=0
（2）（x+2）（x-4）=0
A mathematical problem. Arithmetic equation can be, that is, do not binary linear equation
There are 40% and 60% salt water, to be mixed together to form a concentration of 50% salt water 2000g, how many grams of these two kinds of salt water are needed?
If 40% brine XG is needed, 60% brine (2000-x) g is needed
40% x + 60% (2000-x) = 2000 * 50%
0.4x-0.6x+1200=1000
-0.2x=-200
x=1000
Then 2000-x = 1000
A: the two kinds of brine need 1000g each
If 40% salt water needs x g, then 60% salt water needs 2000-x G
40%x+60%（2000-x）=2000×50%
The solution is: x = 1000
2000-1000=1000
So 1000 grams each
If 60% brine x g is needed, then 40% brine (2000-x) g is needed
60%X+（2000-X）×40%=2000×50%
60%X+800-40%X=1000
20%X=1000-800
X=200÷20%
X=1000
Then, need 40% salt water: 2000-1000 = 1000 grams
A: we need 1000 grams of each of these two kinds of brine.
Arithmetic:
Assuming that the salt water concentration after mixing is 40%, the salt content after mixing is 2000g × 40%.
The actual mixed salt content is 2000g × 50%.
The reason why the total salt quantity is less is that 60% of the salt water is treated as 40% of the salt water, which is equivalent to 20% less of the original 60% salt water concentration. So, 60 percent of the salt water has
（2000×50%-2000×40%）÷（60%-40%）=1000g
40% salt water has 2000-1000 = 1000g
... unfold
Arithmetic:
Assuming that the salt water concentration after mixing is 40%, the salt content after mixing is 2000g × 40%.
The actual mixed salt content is 2000g × 50%.
The reason why the total salt quantity is less is that 60% of the salt water is treated as 40% of the salt water, which is equivalent to 20% less of the original 60% salt water concentration. So, 60 percent of the salt water has
（2000×50%-2000×40%）÷（60%-40%）=1000g
40% salt water has 2000-1000 = 1000g
By using the method of linear equation of one variable
If 40% salt water has x g, then 60% salt water has 2000-x G.
According to the meaning of the title,
40%x + 60%(2000-x) = 2000×50%
The solution is x = 1000
So let 40% salt water have 1000 grams, 60% salt water have 2000-1000 = 1000 grams. Put it away