Factorization of substitution method (x ^ 2-5x + 2) (x ^ 2-5x + 8) + 8 we don't know the substitution method

Factorization of substitution method (x ^ 2-5x + 2) (x ^ 2-5x + 8) + 8 we don't know the substitution method

Let k = x ^ 2-5x, then x ^ 2-5x + 8 = K + 8 (x ^ 2-5x + 2) (x ^ 2-5x + 8) + 8 (K + 2) (K + 8) + 8 = k ^ 2 + 10K + 16 + 8 = k ^ 2 + 10K + 24 = (K + 6) (K + 4) = (x ^ 2-5x + 6) (x ^ 2-5x + 4) = (X-2) (x-3) (x-1) (x-4) = (x-1) (X-2) (x-3) (x-4)
Then, let ^ 2 = ^ 2, t = 5x + 5x-8) + (T + 5x-8)
Factorization exercises (second factorization)
It's the second semester of junior high school
11. Factorization (3a-b) 2-4 (3a-b) (a + 3b) + 4 (a + 3b) 2 = [3a-b-2 (a + 3b)] ^ 2 = (a-7b) ^ 2
12. Factorization (a + 3) 2-6 (a + 3) = (a + 3) (A-3)
13. Factorization (x + 1) 2 (x + 2) - (x + 1) (x + 2) 2 = (x + 1) (x + 2) ABC + ab-4a = a (BC + B-4)
(2)16x2－81＝(4x+9)(4x-9)
(3)9x2－30x＋25＝(3x-5)^2 (4)x2－7x－30＝(x-10)(x+3)
35. Factorization x2-25 = (x + 5) (X-5) 36. Factorization x2-20x + 100 = (X-10) ^ 2
37. Factorization x2 + 4x + 3 = (x + 1) (x + 3)
38. Factorization 4x2-12x + 5 = (2x-1) (2x-5)
39. Factorize the following formulas:
(1)3ax2－6ax＝3ax(x-2)
(2)x(x＋2)－x＝x(x+1)
(3)x2－4x－ax＋4a＝(x-4)(x-a)
(4)25x2－49＝(5x-9)(5x+9)
(5)36x2－60x＋25＝(6x-5)^2
(6)4x2＋12x＋9＝(2x+3)^2
(7)x2－9x＋18＝(x-3)(x-6)
(8)2x2－5x－3＝(x-3)(2x+1)
(9)12x2－50x＋8＝2(6x-1)(x-4)
40. Factorization (x + 2) (x-3) + (x + 2) (x + 4) = (x + 2) (2x-1)
41. Factorization 2ax2-3x + 2ax-3 = (x + 1) (2ax-3)
42. Factorization 9x2-66x + 121 = (3x-11) ^ 2
43. Factorization 8-2x2 = 2 (2 + x) (2-x)
44. Factorization x2-x + 14 = integer cannot be decomposed
45. Factorization 9x2-30x + 25 = (3x-5) ^ 2
46. Factorization - 20x2 + 9x + 20 = (- 4x + 5) (5x + 4)
47. Factorization 12x2-29x + 15 = (4x-3) (3x-5)
48. Factorization 36x2 + 39x + 9 = 3 (3x + 1) (4x + 3)
49. Factorization 21x2-31x-22 = (21x + 11) (X-2)
50. Factorization 9x4-35x2-4 = (9x ^ 2 + 1) (x + 2) (X-2)
51. Factorization (2x + 1) (x + 1) + (2x + 1) (x-3) = 2 (x-1) (2x + 1)
52. Factorization 2ax2-3x + 2ax-3 = (x + 1) (2ax-3)
53. Factorization x (y + 2) - x-y-1 = (x-1) (y + 1)
54. Factorization (x2-3x) + (x-3) 2 = (x-3) (2x-3)
55. Factorization 9x2-66x + 121 = (3x-11) ^ 2
56. Factorization 8-2x2 = 2 (2-x) (2 + x)
57. Factorization x4-1 = (x-1) (x + 1) (x ^ 2 + 1)
58. Factorization x2 + 4x-xy-2y + 4 = (x + 2) (X-Y + 2)
59. Factorization 4x2-12x + 5 = (2x-1) (2x-5)
60. Factorization 21x2-31x-22 = (21x + 11) (X-2)
(1)3x2－6x＝3x(x-2)
(2)49x2－25＝(7x+5)(7x-5)
(3)6x2－13x＋5＝(2x-1)(3x-5)
(4)x2＋2－3x＝(x-1)(x-2)
(5)12x2－23x－24＝(3x-8)(4x+3)
(6)(x＋6)(x－6)－(x－6)＝(x-6)(x+5)
(7)3(x＋2)(x－5)－(x＋2)(x－3)＝2(x-6)(x+2)
(8)9x2＋42x＋49＝(3x+7)^2 .
How to factorize a cubic polynomial of one variable
 
The method of factorization of unary cubic form? Formula,
There is no general method for univariate cubic, but it can be solved by undetermined coefficient method. The premise is that you can guess a solution through the equation, such as x ^ 3-2x + 1. Obviously, this equation has a solution of 1. Then the equation can be written as (x-1) (x ^ 2 + ax + b) and expanded to get x ^ 3 + (A-1) x ^ 2 + (B-A) x-b. so we have a
A chemical material distribution company purchased a batch of chemical raw materials with a total of 7000g, and the purchase price was 30 yuan per kilogram. The price department stipulated that the sales price should not be higher than 70 yuan per kilogram or lower than 30 yuan. The market survey found that the unit price of 70 yuan was 60 kg per day; when the unit price decreased by 1 yuan, the average daily sales was 2 kg more, Other expenses are 400 yuan per day (if the number of days is less than one day, it is calculated as one day). Set the unit price of sales as X Yuan and the average daily profit as y yuan (average daily profit = profit from sales - various expenses)
(1) Find the function relation of Y with respect to X and write out the value range of X
(2) What is the most profitable way of selling or selling according to the highest unit price per day?
Suppose the unit price is reduced by K yuan, then the relationship between the sales unit price and the daily sales volume is 70-k = 60 + 2K (when the unit price is reduced by 1 yuan, the average daily sales volume is increased by 2 kg)
Given that the unit price of sales is x, then x = 70-k. k = 70-x
The average daily profit is y = (70-k) (60 + 2K) - 400, and the profit brought into k is y = - 2x ^ 2 + 200x-400 (30 ≤ x ≤ 70)
The latter is bigger and smaller than others
1,y=-2x^2+200x-400(30≤x≤70）。。。。。。。。。。。。。。。。。。。。。。。。。。。
Alas, the third day of the topic really forget, four years, really can't figure out, alas, regress..
Given that the solution of the equation 2x + MX − 2 = 3 about X is a positive number, then the value range of M is______ .
The original equation is: 2x + M = 3x-6, the solution is: x = m + 6, ∵ x ＞ 0, ∵ m + 6 ＞ 0, ∵ m ＞ - 6
√﹙3x²－4x＋34﹚＋√﹙3x²－4x－11﹚＝9
solve equations
If the substitution order 3x & # 178; - 4x-11 = t, then 3x & # 178; - 4x + 34 = t + 45 √ (T + 45) + √ t = 9 √ (T + 45) = 9 - √ T, then t + 45 = 81-18 √ T + T18 √ t = 36 √ t = 2T = 43x & # 178; - 4x-11 = 43x & # 178; - 4x-15 = 0 (3x + 5) (x-3) = 0x = - 5 / 3, x = 3
3x²－4x－11=a
√(a+45)+√a=9
√(a+45)=9-√a
a+45=81+a-18√a
18√a=36
√a=2
a=3x²－4x－11=4
3x²－4x－15=0
X = 3 or - 5 / 3
Two elementary 3 mathematics solution 1 yuan quadratic equation problem trouble you prawns~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`````````
Solving equation 4 (x-3) ^ 2 = 225
Then there is a difficult problem
Observe the following process of solving the equation, explain its problems, and give the correct solution
（1）X^2=6X
Solution: divide both sides of the equation by X to get x = 6
（2）X^2-2X+1=16
Solution: the original equation is transformed into (x-1) ^ 2 = 16, so X-1 = 4, so x = 5
I'm in trouble. By the way, there's a way to solve the equation
9（X-2）^2=4（X+1）^2
4（X-3）^2=225
（X-3）^2=225/4
x-3=+-15/2
X = - 9 / 2 or x = 21 / 2
（1）X^2=6X
Divide both sides of the equation by X to get x = 6
The problem is that x may be equal to 0, so we can't do this except that x = 0 is actually a solution of the equation, so the answer is x = 0 or x = 6
The correct way is to transfer the term solution;
（2）X^2-2X+1=16
The original equation is transformed to (x-1) ^ 2 = 16, so X-1 = 4, so x = 5
It's OK = - 4
So x = - 3 or x = 5
Factoring problem, mathematical master. Give 50 points to all pairs
(x-y）²-（x-y）³
（x-y） ²-（y-x）³
2（x-y）-.3（y-x）²
4ab（a+b）²-6a ²b（a+b）
（x+y）²（x-y）+（x+y）（x-y）²
2a（a-3）²-6a ² （3-a）+8a（a-3）
24xy²z²(x+y-z)-32xyz(z-x-y)²+8xyz³(z-x-y)
（x-y）^2(1-x+y)
（x-y）^2(1+x-y)
(x-y)(2+3x-3y)
(a+b)(4ab^2-2a^2b)
2x(x+y)(x-y)
2a(3a+5)(a-3)
If 3x & # 178; - 4x + 6 = 9, then 4x & # 178; - 3 / 4x + 6 =? A, 18 B, 12 C, 9 D, 7
3x²-4x+6=9
3x²-4x=3
3(x²-4/3x)=3
x²-4/3x=1
X & # 178; - 4x of 3 + 6 = 7
D