Seven grades mathematics factorization unit examination paper.
First, multiple-choice questions (30 points)
1, the following deformation from left to right belongs to factorization ()
A.2(a-b)= 2a-2b； b . m2- 1 =(m+ 1)(m- 1)；
C.x2-2x+ 1 = x(x-2)+ 1； d . a(a-b)(b+ 1)=(a-ab)(b+ 1)；
2, the following factorization is correct ()
A.2 x2-xy-x = 2x(x-y- 1)； B? xy2+2xy-3y =-y(xy-2x-3)；
C.x(x-y)-y(x-y)=(x-y)2； d . x2-x-3 = x(x- 1)-3；
The final result of 3.2x2-4x+2 factorization is ()
A.2x(x-2)； b . 2(x2-2x+ 1)； c . 2(x- 1)2； d .(2x-2)2；
4. The result of factorization of polynomial p2 (a- 1)+p( 1-a) is ().
A.(a- 1)(p2+p)； b .(a- 1)(p2-p)； c . p(a- 1)(p- 1)； d . p(a- 1)(p+ 1)；
5. If 9x2+kx+25 is completely flat, then the word K is ().
A.？ 30; B? 5; C.30d . 15；
6. Use a simple method to calculate: the value of is ()
A. 1; b； c； d . 2；
7. If a+b=-3 and ab= 1, a+b is equal to ().
A.- 1 1; b . 1 1； c . 7； d .-7；
8, known as a=2009x+2008, b=2009x+2009, c=2009x+20 10, then the polynomial
The value of a2+b2+c2-ab-bc-ac is ().
A.0; b . 1； c . 2； d . 3；
9. If the three sides of a triangle are A, B and C respectively, and a2b-a2c+b2c-b3=0,
Then this triangle is ()
A. isosceles triangle; B. right triangle; C. equilateral triangle; D. the shape of the triangle is uncertain;
10, the square difference between two consecutive odd numbers is always divisible by k, then k is equal to ().
A.4; b . 8； C. 4 or-4; A multiple of D. 8;
Two. Fill in the blanks (24 points)
The common factor of 1 1 and polynomial 9a2x2- 18a3x3-36a4x4 is.
12, factorization: x2-y2-3x-3y=.
13, when x=7, the value of algebraic expression (2x+5) (x+1)-(x-3) (x+1) is.
14. If x- 1 is a factor of x2-5x+c, then c=.
15, if a2+2a+b2-6b+ 10=0, then a=, b=.
16, if x+y= 1, the value of the algebraic expression is.
17. When x= 10 and y=9, the value of the algebraic expression x2-y2 is.
18, given that a+b=3 and a-b=- 1, the value of a2-b2 is.
Iii. Answering questions (46 points)
19, (12 point) factorization:
( 1) 2m-2m5 (2)
(3)x3-2 x2+x(4)(m+2n)2-6(m+2n)(2m-n)+9(n-2m)2
20.(6 points) Given 2a-b=, find the value of 12a2- 12ab+3b2.
2 1, (6 points) If A, B and C are three sides of △ABC, and a2+b2+c2-ab-bc-ac=0, explore.
△ The shape of △ABC and explain why.
22.(6 points) Farmer A has two plots, one is a square with a side length of a meter and the other is a rectangle with a length of c meters and a width of b meters; Farmer b also has two plots of land, both rectangular, a meter wide, b meters long and c meters long. This year, the two farmers are investing in breeding. To this end, they are going to replace four plots with a width of (a+b) m. In order to make the changed land area equal to the total area of the original four plots, what should be the length of the land after replacement?
23.(8 points) Before answering the questions raised, read the following factorization process:
1+x+x(x+ 1)+x(x+ 1)2 =( 1+x)[ 1+x(x+ 1)]=( 1+x)2( 1+x)=( 1+x)3
(1) The factorization method above is * * * is the number of applications.
(2) Factorization:1+x+x (x+1)+x (x+1) 2+? +x(x+ 1)20 10, the above methods need to be applied many times.
The result is.
(3) Factorization:1+x+x (x+1)+x (x+1) 2+? +x(x+ 1)n(n is a positive integer)
24.(8 points) Read the factorization method below, and then complete the following questions according to the examples:
In the factorization process of some polynomials, through? Alternative method? You can change a polynomial with complex form into a polynomial with simple form and easy decomposition, so that the problem can be simplified and solved quickly.
For example, factorization (x2+x-2)(x2+x- 12)+24.
Solution: Let y= x2+x-2, then x2+x- 12=y- 10, so
(x2+x-2)(x2+x- 12)+24 = y(y- 10)+24 = y2- 10x+24 =(y-4)(y-6)
Namely: (x2+x-2) (x2+x-12)+24 = (x2+x-2-4) (x2+x-2-6).
=( x2+x-6)( x2+x-8)
=(x-2)(x+3)( x2+x-8)
Factorization is carried out as above: (x2+3x-2)(x2+3x+4)- 16.
The seventh grade mathematics factorization unit examination paper reference answer
1. 1，b； 2、C； 3、C； 4、C； 5、A；
6、C； 7、C； 8、D； 9、A； 10、B；
Second, 1 1, 9a2x2 12, (x-y-3) (x+y); 13、-6; 14、4; 15、- 1,3;
16、 ; 17、 19; 18、-3;
Iii. 19, (1) Original formula = 2m (1+m2) (1+m); (2) The original formula =;
(3) The original formula = x (x-1) 2; (4) Original formula = 25 (n-m) 2;
20. The original formula =3(4a-4ab+b)=3(2a-b) 2=3? =
2 1 and △ABC are equilateral triangles.
∫a2+B2+C2-a b-BC-AC = 0, which means 2(a2+b2+c2-ab-bc-ac)=0.
a2-2ab+B2+B2-2bc+C2+a2-2ac+C2 = 0？ (a-b) 2+(b-c) 2+(a-c) 2=0
? A=b, b=c, a=c, that is, a=b=c is equal on three sides.
22. The area of the original four plots: A2+AB+BC+AC = A (A+B)+C (A+B) = (A+C) (A+B).
The width of the exchanged land is (a+b) m, so the length of the exchanged land is (a+c) m,
23, (1) common factor method, 2; 20 10，(x+ 1) 20 1 1
(3)(x+ 1) n+ 1
24. Let x2+3x-2=y,
(x2+3x-2)(x2+3x+4)- 16 = y(y+6)- 16 = y2+6y- 16 =(y-2)(y+8)
(x2+3x-2)(x2+3x+4)- 16 =(x2+3x-4)(x2+3x+6)=(x- 1)(x+4)(x2+3x+6)
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