If u = R, a = {x | x ^ 2 + 3x-4 > 0}, B = {x | - 4 ≤ x ≤ - 1}, find a ∩ B, AUB, CUA?

If u = R, a = {x | x ^ 2 + 3x-4 > 0}, B = {x | - 4 ≤ x ≤ - 1}, find a ∩ B, AUB, CUA?

x²+3x-4>0
So a is x1
therefore
A ∩ B = empty set
AUB={x|x1}
CuA={x|-4
A = {x | x 〉 1 or X 〈 - 4}
Then a ∩ B = empty set, a ∪ B = {x | x ≤ - 1 or X ＞ 1}, CUA = {x | - 4 ≤ x ≤ 1}
Let u be a complete set = R, a = {x | (4x-1) ^ 2 ≥ 81}, B = {x | (x + 3) ≥ 3}, then CUA ∩ cub =?
A＝｛x|(4x-1)^2≥81},
x> = 5 / 2 or X
Given a = {x | - 1 ≤ x ≤ 3}, B = {x | x2}, the complete set u = R, find a ∪ B, (CUA) ∩ cub
A ∪ B = {x | - 1 ≤ x2 ≤ 3}, (CUA) ∩ (cub) = empty set
Factorization test answers
Fill in the blanks:
1. In (x + y) (X-Y) = x2-y2, the deformation from left to right is. The deformation from right to left is
2. The factorization factor 2XY - XZ =
3. Given m + n = 5, Mn = - 14, then m2N + Mn2 =
4. Decomposition factor: M 2 (x-2y) - M 3 (2y-x) = m 2 (x-2y)
5. Decomposition factor: - 5ab2 + 10a2b-15ab =
6. It is known that the surface area of a rectangle is 4m2-25n2, and the length of one side is 2m-5n
7、x2— +9y2=（x— ）2.
8. Please write a polynomial so that it can first "raise the common factor" and then "use the formula" to decompose the factor. Your polynomial is, the result of factoring the factor is
9. Among the following left to right deformations, the one that does not belong to factorization is ():
A、x5+x4=x4（x+1）； B、—2a2+4ab= —2a（a—2b）；
C、mx+my+xy=m（x+y）+xy； D、a2—b2=（a+b）（a—b）；
10. The following factorization is correct ():
A、2a2—3ab+a=a（2a—3b）； B、—x2—2x=—x（x—2）；
C、2πR—2πr=π（2R—2r）； D、5m4+25m2=5m2（m2+5）
11. The common factor of polynomial-6xyz + 3xy2-9x2y is ():
A、—3x； B、3xz； C、3yz； D、—3xy.
12. In the following polynomials, the one that cannot be decomposed by the square difference formula is ():
A、a2b2—1； B、4—0.25m4； C、1+a2； D、—a4+1.
13. In the following factorization, the error is ():
A、1—9x2=（1+3x）（1—3x）； B、a2—a+=（a—）；
C、—mx+my= —m（x—y）； D、x2+2xy+y=（x+2y）2.
14. In the following algebraic expressions, the complete square form is ():
①2x2—2x+1； ②x2—xy+y2；③4x4+4x+1；④9x2+16y2—12xy；
A、①②； B、②③； C、③④； D、①④；
15. If 4x2 + KX + 25 is a complete square, then k equals ():
A、±10； B、20； C、—20； D、±20；
16. When a student carelessly decomposes the factor, he contaminates the two numbers in the equation a - * = (a + 9) (a + 3) (a - *). Then you think that the group of numbers corresponding to *, ● in the equation is ():
A、9,3； B、81,3； C、81,9； D、27,3.
3、 Answer:
17. Decomposition factor: - 12x3y2 + 18x2y3-6xy;
18. Decomposition factor: m3n2-m5;
19. Decomposition factor: 9x2-6x + 1;
20. Decomposition factor: (a + B + C) 2 - (a + B-C) 2;
4、 Application of knowledge:
21. Factorization calculation
3.14×552—3.14×452；
22. Factorization calculation
20082—2008×16+64；
23. Solve the equation by factorization
x2—16=0；
24. As shown in the figure, on the circular steel plate with radius r, remove the four small circles with radius R. if r = 7.8cm, r = 1.. 1cm, please apply your knowledge and calculate the remaining area in the simplest way. (π is taken as 3.14, and the result retains three significant digits)
5、 Explore Paradise:
25. Please observe the following problem-solving process:
Factorization: x4-6x2 + 1
x4—6x2+1= x4—2x2—4x2+1
=（x4—2x2+1）—4x2
=（x2—1）2—（2x）2
=（x2—1+2x）（x2—1—2x）
The above method of factoring is called the method of factoring. Please use the method of Factoring: a4-9a2 + 16
6、 Comprehensive questions:
27. It is known that the factorization of the quadratic trinomial x 2-ax + B is (x-1) (x-3)
(1) Find the value of a and B;
(2) If a and B are two right sides of a right triangle, find the length of its hypotenuse
(3) Try to draw the image of y = ax + B in the given coordinate system
Your square and cubic are not very clear. I did it, but I don't know if the topic I understand is what you want, so you should have a look at it for yourself
1. In (x + y) (X-Y) = x2-y2, the deformation from left to right is X & sup2; - Y & sup2;, and the deformation from right to left is (x + y) * (X-Y)
2. The factorization factor 2XY - XZ = x (2Y - z)
3. Given m + n = 5, Mn = - 14, then M 2n + Mn 2 = Mn (M + n) = - 14 * 5 = - 70
4. Decomposition factor: M2 (x-2y) - m3 (2y-x) = M2 (x-2y). (x-2y) - M (2y-x) = x-2y x + mx-2y-m2y = x-2y (1 + m) X-2 (1 + m) y = x-2y
5. The decomposition factor is - 5ab2 + 10a2b-15ab = - 5ab (b-2a + 3)
6. It is known that the surface area of a rectangle is 4m2-25n2. One side is 2m-5n long, and the other side is 2m + 5N long
7. X2 - + 9y2 = (x -) 2
8. Please write a polynomial so that it can first "raise the common factor" and then "use the formula" to decompose the factor. Your polynomial is 2A & sup2; - 8b & sup2;, and the result of factoring the factor is 2 (A & sup2; - 4B & sup2;) = 2 (a + 2b) (a-2b)
2、 Multiple choice questions:
9. Among the following left to right deformations, the one that does not belong to factorization is (c)
A、x5+x4=x4（x+1）； B、—2a2+4ab= —2a（a—2b）；
C、mx+my+xy=m（x+y）+xy； D、a2—b2=（a+b）（a—b）；
10. The correct decomposition factor is (d)
A、2a2—3ab+a=a（2a—3b）； B、—x2—2x=—x（x—2）；
C、2πR—2πr=π（2R—2r）； D、5m4+25m2=5m2（m2+5）
11. The common factor of the polynomial-6xyz + 3xy2-9x2y is (d)
A、—3x； B、3xz； C、3yz； D、—3xy.
12. In the following polynomials, (c) cannot be decomposed by the square difference formula:
A、a2b2—1； B、4—0.25m4； C、1+a2； D、—a4+1.
13. In the following factorization, the wrong one is (D is wrong, B is incomplete, you can see for yourself)
A、1—9x2=（1+3x）（1—3x）； B、a2—a+=（a—）；
C、—mx+my= —m（x—y）； D、x2+2xy+y=（x+2y）2.
14. In the following algebraic expressions, (c) is a complete square expression:
①2x2—2x+1； ②x2—xy+y2；③4x4+4x+1；④9x2+16y2—12xy；
A、①②； B、②③； C、③④； D、①④；
15. If 4x2 + KX + 25 is a complete square, then K is equal to (d)
A、±10； B、20； C、—20； D、±20；
16. When a student carelessly decomposes the factor, he contaminates the two numbers in the equation a - *? = (a + 9) (a + 3) (a - *). Then you think that the group of numbers corresponding to *, ● in the equation is (is this problem incomplete)
A、9,3； B、81,3； C、81,9； D、27,3.
3、 Answer:
17. Decomposition factor: - 12x3y2 + 18x2y3-6xy;
The original formula = - 6xy (2x & sup2; y-3xy & sup2; + 1)
18. Decomposition factor: m3n2-m5;
The original formula = m cubic (n & sup2; - M & sup2;) = m cubic * (n + m) * (n-m)
19. Decomposition factor: 9x2-6x + 1;
The original formula = (3x + 1) & sup2;
20. Decomposition factor: (a + B + C) 2 - (a + B-C) 2;
The original formula = (a + B + C + A + B-C) (a + B + C-A-B + C) = (2a + 2b) (2C) = 2 (a + B + C)
4、 Application of knowledge:
21. Factorization calculation
3.14×552—3.14×452；
Original formula = 3.14 (552-452) = 3.14 * 100 = 314
22. Factorization calculation
20082—2008×16+64；
The original formula = (2008 + 8) & sup2; = 2016 & sup2; = 4064256
23. Solve the equation by factorization
x2—16=0；
(x-4) (x + 4) = 0, so x = plus or minus 4
24. As shown in the figure, on the circular steel plate with radius r, remove the four small circles with radius R. if r = 7.8cm, r = 1.. 1cm, please apply your knowledge and calculate the remaining area in the simplest way. (π is taken as 3.14, and the result retains three significant digits)
Sorry, I can't understand the meaning of this question
5、 Explore Paradise:
25. Please observe the following problem-solving process:
Factorization: x4-6x2 + 1
x4—6x2+1= x4—2x2—4x2+1
=（x4—2x2+1）—4x2
=（x2—1）2—（2x）2
=（x2—1+2x）（x2—1—2x）
The above method of factoring is called the method of factoring. Please use the method of Factoring: a4-9a2 + 16
a4-8a²-a²+16=（a²-4）²-a²=（a²-4-a）（a²-4+a）
6、 Comprehensive questions:
27. It is known that the factorization of the quadratic trinomial x 2-ax + B is (x-1) (x-3)
(1) Find the value of a and B, and the meaning is: X & sup2; - 4x + 3 = x & sup2; - ax + B, then: a = 4, B = 3
(2) If a and B are two right sides of a right triangle, find the length of the hypotenuse. Hypotenuse = root sign (a square + b square) = 5
(3) Try to draw an image of y = ax + B in a given coordinate system. I can't draw a picture. AB knows that you can draw it
Let a-2b be the square ab of 2a and B be the square + 3 of A
A-2b = 2A ^ 2-AB, B = - A ^ 2, so a = 2B + 2A ^ 2-AB = - 2A ^ 2 + 2A ^ 2-AB = - ab
(x+1)(x+2)(x+3)(x+4)-120
(x+1)(x+2)(x+3)(x+4)-120 =[(x+4)(x+1)][(x+2)(x+3)]-120 =(x^2+5x+4)(x^2+5x+6)-120=(x^2+5x)^2+10(x^2+5x)+24-120=(x^2+5x)^2+10(x^2+5x)-96=(x^2+5x+16)(x^2+5x-6)=(x^2+5x+16)(x+6)(x-1)
(2a + 2b) (half a - half b)
=2(a+b) ×1/2(a-b)
=(a+b)(a-b)
=a²-b²
(2a+2b)(a/2-b/2)
=a²-ab+ab-b²
=a²-b²
A factorization problem in grade one of junior high school
-49X^2+14X-1+y^2
-49X^2+14X-1+y^2
=y^2-(49x^2-14x+1)
=y^2-(7x-1)^2
=(y-7x+1)(y+7x-1)
[(2a + b) 2 + (2a + b) (b-2a) - 6B] / 2B, where a and B satisfy | a + half | + √ B-3 = 0
|A + half | + √ B-3 = 0
Then:
a+1/2=0
a=-1/2
b-3=0
B=3
[（2a+b）2+（2a+b）（b-2a）-6b]/2b
=(4a²+4ab+b²+b²-4a²-6b)/2b
=b+2a-3
=3-1-3
=-1
Give me some simple factorization problems,
(x+y)^2-(a+b)^2=(x+y+a+b+)(x+y-a-b)x²-4y²+x-2y=(x-2y)(x+2y)+(x-2y)=(x-2y)(x+2y+1) x^2(a+b-c)-2(c-b-a)=x²(a+b-c)+2(a+b-c)=(a+b-c)(x²+2)