Factorization 6x & # 178; + 7x + 2

Factorization 6x & # 178; + 7x + 2

（2x+1）（3x+2）
Given that the solutions X and y of the system of equations X-Y = 3 2x + KY = 8 are opposite to each other, find the value of K
x. Y is opposite to each other
x-y=3
x-(-x)=3
x=1.5
y=-1.5
2x+ky=8
2×1.5-1.5k=8
k=-10/3
Because X-Y = 3, and X and y are opposite numbers, x = 3 / 2, y = - 3 / 2,
Take x = 3 / 2, y = - 3 / 2 and bring it in
2x+ky=8
K = - 10 / 3
x+y=o x=1.5 3+ky=8 y=-1.5 k=-2
It is known that the factorization result of the quadratic trinomial 3x & # 178; + MX + n is (3x + 2) multiplied by (x-1) to find the value of M.N
 
Factorization - 6x & # 178; + 7x + 20 and 35x & # 178; + 26x + 3
Formula method or extraction of common factor method
-6x²+7x+20
-3 4
X
25
Original formula = (- 3x + 4) (2x + 5)
35x²+26x+3
53
X
71
Original formula = (5x + 3) (7x + 1)
It is known that the equations 2x + KY = 16, x-2y = 0 have natural number solutions
It is known that the equations 2x + KY = 16, x-2y = 0 have natural number solutions?
The solution of the system of equations is x = 2Y, y = 16 / (4 + k), so (4 + k) is a divisor of 16, which can be equal to + 1, + 2, + 4, + 8, + 16 negative divisors. So k = - 3, - 2,0,4,12
x=2y,2x+ky=16,4y+ky=16,(4+k)y=16,x∈N*,y∈N*,∴y｜16,y=1,2,4,8,16,∴k=12,4,0,-2,-3.
It is known that the factorization of quadratic trinomial 2x & # - 9x + K has a factor x-3. Try to find the value of K and another factor
K = 9, and the factor is 2x-3
9. Reply: 2x minus 3
Factorization 6x & # 178; - 7x-24 = 0
Cross multiplication
2x +3
3x -8
So we get 2 (- 8) + 3 * 3 = - 16 + 9 = - 7
therefore
6x^2-7x-24=0
(2x+3)(3x-8)=0
x1=-3/2,x2=8/3
（2x+3）（3x-8）=0
Given that the solution of the equations {x-2y = 3, {2x + KY = 8, satisfies x = y, find the value of K
X=y
Substituting x-2y = 3
x-2x=3
So x = - 3
y=x=-3
Substituting 2x + KY = 8
-6-3k=8
So k = - 14 / 3
Given that two of the equations 2x & # 178; + PX + q = 0 about X are x = 2, x = - 3, then the quadratic trinomial 2x & # 178; + PX + Q can be factorized into
Substituting x = 2, x = - 3 into the equation, we get P = 2, q = - 12
2x²+2x-12=2(x+3)(x-2)
Substituting x = 2, x = - 3 into the equation, we get P = 2, q = - 12
2x²+2x-12=2(x+3)(x-2)
The factorization of 6x & # 178; - 7x + 3
6X & # 178; - 7x + 3 cannot decompose factors in the range of real numbers