First, fill in the blanks:
2.(a-3)(3-2a)= _ _ _ _ _ _ _(3-a)(3-2a)；
12. if m2-3m+2 = (m+a) (m+b), then a = _ _ _ _ _ _ and b = _ _ _ _ _ _
15. When m = _ _ _ _ _, x2+2 (m-3) x+25 is completely flat.
Second, multiple-choice questions:
1. Among the following factorization results, the correct one is
[ ]
A.a2b+7ab-b=b(a2+7a)
b . 3x2y-3xy-6y = 3y(x-2)(x+ 1)
C.8xyz-6x2y2=2xyz(4-3xy)
D.-2a2+4ab-6ac=-2a(a+2b-3c)
2. The factorization factor of polynomial m (n-2)-m2 (2-n) is equal to
[ ]
A.(n-2)(m+m2) B.(n-2)(m-m2)
(n-2)(m+ 1)d(n-2)(m- 1)
3. In the following equation, belongs to the factorization is
[ ]
A.a(x-y)+b(m+n)=ax+bm-ay+bn
b . a2-2ab+B2+ 1 =(a-b)2+ 1
C.-4a2+9b2=(-2a+3b)(2a+3b)
D.x2-7x-8=x(x-7)-8
4. In the following types, factors can be decomposed by square difference formula.
[ ]
A.a2+b2 B.-a2+b2
C.-a2-b2 D.-(-a2)+b2
5. If 9X2+Mxy+ 16Y2 is a completely flat mode, the value of m is
[ ]
A.- 12 B. 24
C. 12
6. By decomposing the polynomial an+4-an+ 1
[ ]
(a4-a) B.an- 1(a3- 1)
c . an+ 1(a- 1)(a2-a+ 1)d . an+ 1(a- 1)(a2+a+ 1)
7. if A2+A =- 1, the value of A4+2A3-3A2-4A+3 is
[ ]
a8b . 7
c 10d 12
8. Assuming that x2+y2+2x-6y+ 10 = 0, the values of x and y are respectively
[ ]
A.x= 1，y=3 B.x= 1，y=-3
C.x=- 1，y=3 D
9. Factorization (m2+3m) 4-8 (m2+3m) 2+ 16.
[ ]
A.(m+ 1)4(m+2)2 b .(m- 1)2(m-2)2(m2+3m-2)
C.(m+4)2(m- 1)2d .(m+ 1)2(m+2)2(m2+3m-2)2
10. Factorization X2-7x-60 is obtained.
[ ]
A.(x- 10)(x+6)b .(x+5)(x- 12)
C.(x+3)(x-20) D.(x-5)(x+ 12)
1 1. Factorization 3x2-2xy-8y2 is obtained.
[ ]
A.(3x+4)(x-2) B.(3x-4)(x+2)
C.(3x+4y)(x-2y) D.(3x-4y)(x+2y)
12. Factorizing A2+8ab-33b2 to obtain
[ ]
A.(a+ 1 1)(a-3)b .(a- 1 1b)(a-3b)
C.(a+ 1 1b)(a-3b)d .(a- 1 1b)(a+3b)
13. factorize X4-3x2+2 to get.
[ ]
A.(x2-2)(x2- 1)b .(x2-2)(x+ 1)(x- 1)
C.(x2+2)(x2+ 1)d .(x2+2)(x+ 1)(x- 1)
14. the decomposable factor of polynomial x2-ax-bx+ab is
[ ]
A.-(x+a)(x+b) B.(x-a)(x+b)
C.(x-a)(x-b) D.(x+a)(x+b)
15. For a quadratic trinomial of X, the coefficient of the x2 term is 1, and the constant term is-12, which can decompose the factors. Such a quadratic trinomial is
[ ]
A.x2-11x-12 or x2+112.
B.x2-x- 12 or x2+x- 12
C x2-4x- 12 or x2+4x- 12
D. All the above can be done.
16. Exclude the following x3-x2-x+ 1, x2+y-xy-x, x2-2x-y2+ 1, (x2+3x) 2-(2x+ 1) 2.
[ ]
A. 1
C.3 D.4
The factorization factor of17.9-x2+12xy-36y2 is
[ ]
A.(x-6y+3)(x-6x-3)
B.-(x-6y+3)(x-6y-3)
C.-(x-6y+3)(x+6y-3)
D.-(x-6y+3)(x-6y+3)
18. The following factorization error is
[ ]
A.a2-bc+ac-ab=(a-b)(a+c)
B.ab-5a+3b- 15=(b-5)(a+3)
C.x2+3xy-2x-6y=(x+3y)(x-2)
d . x2-6xy- 1+9 y2 =(x+3y+ 1)(x+3y- 1)
19. It is known that A2X2 2x+B2 is completely flat, and both A and B are not zero, so the relationship between A and B is
[ ]
A. reciprocal or negative reciprocal
C. Equal number D. Arbitrary rational number
20. Decomposition of X4+4, the correct conclusion is
[ ]
A. factor B. There is a factor x2+2x+2.
C.(xy+2)(xy-8) D.(xy-2)(xy-8)
The factorization factor of 2 1.A4+2A2 B2+B4-A2B 2 is
[ ]
A.(a2+B2+ab)2b .(a2+B2+ab)(a2+B2-ab)
C.(a2-B2+ab)(a2-B2-ab)d .(a2+B2-ab)2
22.-(3x- 1) (x+2y) is the decomposition result of which of the following polynomials?
[ ]
A.3x2+6xy-x-2y B.3x2-6xy+x-2y
C.x+2y+3x2+6xy D.x+2y-3x2-6xy
23.64a8-B2 factorization is as follows
[ ]
A.(64 a4-b)(a4+b)b .( 16 a2-b)(4a 2+b)
C.(8a4-b)(8a4+b) D.(8a2-b)(8a4+b)
24.9 the factorization of (x-y) 2+12 (x2-y2)+4 (x+y) 2 is as follows
[ ]
A.(5x-y)2 B.(5x+y)2
C.(3x-2y)(3x+2y) D.(5x-2y)2
25.(2y-3x) 2-2 (3x-2y)+ 1 factorization is
[ ]
A.(3x-2y- 1)2 b .(3x+2y+ 1)2
C.(3x-2y+ 1)2d .(2y-3x- 1)2
26. the factorization of (a+b) 2-4 (a2-B2)+4 (a-b) 2 is as follows
[ ]
A.(3a-b)2 B.(3b+a)2
C.(3b-a)2 D.(3a+b)2
27. the decomposition factor of a2 (b+c) 2-2ab (a-c) (b+c)+B2 (a-c) 2 is
[ ]
Communication (a+b)2
C.c2(a+b)2 D.c2(a-b)
28. If the factor of 4xy-4x2-y2-k is (1-2x+y), the value of k is
[ ]
A.0 B. 1
C.- 1 D.4
29. The factorization factor 3a2x-4b2y-3b2x+4a2y is correct.
[ ]
A.-(a2+B2)(3x+4y)b .(a-b)(a+b)(3x+4y)
C.(a2+B2)(3x-4y)d .(a-b)(a+b)(3x-4y)
30. The factorization factor 2a2+4ab+2b2-8c2 is correct.
[ ]
A.2(a+b-2c) B.2(a+b+c)(a+b-c)
C.(2a+b+4c)(2a+b-4c)d . 2(a+b+2c)(a+b-2c)
Third, factorization:
1 . m2(p-q)-p+q；
2 . a(a b+ BC+AC)-ABC；
3 . x4-2y 4-2x3y+xy3；
4 . ABC(a2+B2+C2)-a3bc+2 ab2c 2；
5 . a2(b-c)+B2(c-a)+C2(a-b)；
6.(x2-2x)2+2x(x-2)+ 1；
7.(x-y)2+ 12(y-x)z+36z 2；
8 . x2-4ax+8ab-4 B2；
9.(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx)；
10.( 1-a2)( 1-B2)-(a2- 1)2(B2- 1)2；
1 1.(x+ 1)2-9(x- 1)2；
12.4 a2 B2-(a2+B2-C2)2；
13 . ab2-ac2+4ac-4a；
14 . x3n+y3n；
15.(x+y)3+ 125；
16.(3m-2n)3+(3m+2n)3；
17 . X6(x2-y2)+y6(y2-x2)；
18.8(x+y)3+ 1；
19.(a+b+c)3-a3-B3-C3；
20 . x2+4xy+3 y2；
2 1 . x2+ 18x- 144；
22 . x4+2 x2-8；
23.-M4+ 18 m2- 17；
24 . X5-2x 3-8x；
25 . x8+ 19x 5-2 16x 2；
26.(x2-7x)2+ 10(x2-7x)-24；
27.5+7(a+ 1)-6(a+ 1)2；
28.(x2+x)(x2+x- 1)-2；
29 . x2+y2-x2 y2-4xy- 1；
30.(x- 1)(x-2)(x-3)(x-4)-48；
3 1 . x2-y2-x-y；
32 . ax2-bx2-bx+ax-3a+3b；
33 . M4+m2+ 1；
34 . a2-B2+2ac+C2；
35 . a3-ab2+a-b；
36.625 B4-(a-b)4；
37 . X6-y6+3x2y 4-3x4y 2；
38 . x2+4xy+4 y2-2x-4y-35；
39 . m2-a2+4ab-4b 2；
40.5m -5n-m2+2mn-n2.
IV. Proof (evaluation):
1. Given a+b = 0, find the value of a3-2b3+a2b-2ab2.
2. Prove that the product of four consecutive natural numbers plus 1 must be a complete square number.
3. Proof: (AC-BD) 2+(BC+AD) 2 = (A2+B2) (C2+D2).
4. Given a = k+3, b = 2k+2 and c = 3k- 1, find the value of a2+b2+c2+2ab-2bc-2ac.
5. If x2+MX+n = (x-3) (x+4), find the value of (m+n) 2.
6. When a is a value, the polynomial x2+7xy+AY2-5x+43y-24 can be decomposed into the product of two linear factors.
7. If x and y are arbitrary rational numbers, compare the sizes of 6xy and x2+9y2.
8. The square difference between two consecutive even numbers is a multiple of 4.
Reference answer:
First, fill in the blanks:
7.9，(3a- 1)
10.x-5y，x-5y，x-5y，2a-b
1 1.+5,-2
12.- 1, 2 (or -2, 1)
14.bc+ac，a+b，a-c
15.8 or -2
Second, multiple-choice questions:
1.B 2。 C 3。 C 4 explosive B 5。 B 6。 D 7。 An eight. C 9。 D 10。 B 1 1。 C 12。 C 13。 B 14。 C 15。 D 16。 B 17。 B 18。 D 6543 8+09。 A 20. B 2 1。 B 22。 D 23。 C 24。 A handful of 25. A 26. C 27。 C 28。 C 29。 D 30。 D
Third, factorization:
1.(p-q)(m- 1)(m+ 1)。
8.(x-2b)(x-4a+2b)。
1 1.4(2x- 1)(2-x)。
20.(x+3y)(x+y)。
2 1.(x-6)(x+24)。
27.(3+2a)(2-3a)。
3 1.(x+y)(x-y- 1)。
38.(x+2y-7)(x+2y+5)。
IV. Proof (evaluation):
2. Hint: Let four consecutive natural numbers be n, n+ 1, n+2 and n+3.
6. Prompt: A =- 18.
∴a=- 18.