How to factorize 2x ^ 3 + (2a + 23) x & sup2; + (10-7a) x + 3a-11?

How to factorize 2x ^ 3 + (2a + 23) x & sup2; + (10-7a) x + 3a-11?

=2x^3+2ax^2+23x^2+10x-7ax+3a-11
=2x^3+23x^2+10x-11+a(2x^2-7x+3)
=2x^3-x^2+24x^2+10x-11+a(2x-1)(x-3)
=x^2(2x-1)+(2x-1)(12x+11)+a(2x-1)(x-3)
=(2x-1)(x^2+12x+11+ax-3a)

1. Factorization (1) 3A square b square - 6B cube C (2) x cube - 16x (3) (M-3) square - (M + 2) square (4) 2 calculation (2ax-n)
The fourth is 3x (6x cube, y square - 4xy cube) / (- 6x cube, y Square)
If (1) = how much

3a^2b^2-6b^3c=3b^2(a^2-2bc)(2)x^3-16x=x*(x^2-16)=x(x+2)(x-2)(3)(m-3)^2-(m+2)^2=(m-3+m+2)(m-3-m-2)=5-10m(4)3x(6x^3y^2-4xy^3)÷(-6x^3y2)=3x(-1+2y/3x^2)=-3x+2y/x

Given that a ^ 2x ^ 2 - (3a ^ 2-8a) x + 2A ^ 2-13a + 15 = 0 has at least one integer root, find the value of A
I didn't say a was an integer.

The original equation can be reduced to a ^ 2x ^ 2 - (3a ^ 2-8a) x + (a-5) (2a-3) = 0
It is further reduced to [ax - (2a-3)] [ax - (a-5)] = 0
When a = 0, the original equation is changed to 15 = 0
When a ≠ 0, X1 = (2a-3) / A, X2 = (a-5) / A
Namely: X1 = 2 - (3 / a) x2 = 1 - (5 / a)
A = 1 or 3 or 5

Using factorization to solve the equation: ① 8A ^ 2-2a = 0 ② (x + 2) ^ 2 = (2x-1) ^ 2
Come on, today!

①8a^2-2a=0
If both sides of the original equation are divided by 2, we can get:
4a²-a=0
The factorization is as follows
a(4a-1)=0
The solution is a = 0 or a = 1 / 4
②（x+2）^2=(2x-1)^2
The original equation can be reduced to:
(x+2)²-(2x-1)²=0
The factorization is as follows
(x+2+2x-1)(x+2-2x+1)=0
That is, (3x + 1) (- x + 3) = 0
The solution is x = - 1 / 3 or x = 3

Does the car run 60 miles per hour or 60 kilometers per hour?
What's the meaning of 60 miles per hour / 60 yards per hour?

Not 60 kilometers an hour, but 60 miles
Usually, some people say that the speed of a vehicle is how many yards per mile. This is actually a saying in Hong Kong and Taiwan. In fact, it means mile / hour, that is, mile, 1mile = 1.6km. Therefore, a speed of 60mph should be about 96km / h

Fill in the appropriate length unit. The thickness of a dime is about 1 (). The thickness of 8 books is about 1 ()
The thickness of our mathematics book is about 8 (). The length of a nail is about 54 (). The thickness of a rubber is about 12 (). The length of a picture nail is about 1 (). The width of an exercise book is about 15 (). The length of your middle finger is about 6 ()

The thickness of our mathematics book is about 8 (mm). The length of a nail is about 54 (mm). The thickness of a rubber is about 12 (mm). The length of a picture nail is about 1 (CM). The width of an exercise book is about 15 (CM). The length of your middle finger is about 6 (CM)
The thickness of a dime is about 1 (mm). The thickness of eight book papers is about 1 (mm)

The proof of Lagrange mean value theorem on higher numbers
How to find auxiliary function when proving Lagrange mean value theorem with Rolle mean value theorem

Generally speaking, there is no definite rule and strong skill in constructing auxiliary function, but there is no general rule to follow. For example, Lagrange's mean value theorem and Cauchy's mean value theorem, first of all, they are all about the problem of function mean value, and this problem has a basic theorem: Rolle's theorem, Therefore, the auxiliary function to be constructed should satisfy the conditions of Rolle's theorem as much as possible. That is to say, the form of the function to be constructed when the values of the functions at x = A and x = B are equal and its derivative is equal to 0 is the form of the expression in the theorem to be proved, First of all, draw a diagram, you can notice that Lagrange's mean value theorem is actually just a rotation angle of the graph in Rawl's theorem. Write out the equation passing through points (a, f (a)), (B, f (b)): F (x) - f (a) = {[f (b) - f (a)] / (B-A)} (x-a). You can see that if f (x) = f (x) - f (a) - {[f (b) - f (a)] / (B-A)} (x-a), then f (a) = f (b), and f '(x) = f' (x) - [f (b) - f (a)] / (B-A), Let f '(x) = 0 is the expression of Lagrange mean value theorem

Two 1 square decimeter squares can be used to form a rectangle. How many decimeters is the perimeter and area of the rectangle? (please draw a diagram)

As shown in the figure, because 1 × 1 = 1 (square decimeter), the side length of the square is 1 decimeter; after assembling, the length of the rectangle is 1 × 2 = 2 (decimeter), the width is 1 decimeter; (2 + 1) × 2 = 6 (decimeter); 2 × 1 = 2 (square decimeter); answer: the perimeter of the rectangle is 6 decimeters, the area is 2 square decimeters

4x2 + MX + 49 is a complete square, then M=______ ．

∵ 4x2 + MX + 49 is a complete square formula, ∵ M = ± 28

F1F2 is the two focal points of the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, P is on the ellipse, △ pf1f2 is a right triangle, find the point P coordinate

In the first case, if the angle pf1f2 or pf2f1 is 90 degrees, then the coordinates of point P are (- radical 5,4 / 3) or (radical 5,4 / 3) or (- radical 5, - 4 / 3) or (radical 5, - 4 / 3). In the second case, if the angle P is 90 degrees, then the coordinates of point P are (x, y), then: by x2 / 9 + Y2 / 4 = 1 and