1. There are 8 algebraic expressions, 1 fractional expressions and 2 irrational expressions in the following formula.
5、ba、34 a-2b、S =vt、3π、m、3x-6 & gt； 5 、-5x2 y z 10、a+3a2- 1、x2+ 1。
2. The highest coefficient of polynomial 1-x24 is-14.
3. If a+b+c=0, simplify A (1b+1c)+B (1c+1a)+C (1b).
4, if there are 2007 students in a row, according to the law of 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 5, 4, 3, 2, 1, then 2007 ...
5. There are five secondary radicals, which are divided into the following categories.
①-3②m2+ 1③27④-x2- 1⑤-(-3)3⑥a+ 1(a & lt； -2) ⑦m2-2m+7 ⑧ 16
6. The range of the independent variable x of the function y = 2x+3 1-x+ 1 is x≥- 1 and x≠0.
7. If the algebraic expression x+ 1x+2 ÷ x+3x+4 is meaningful, the range of x is X≦-2 and X≦-3 and X≦-4.
8. Give the following calculation or simplification: (1)(a2)4= a6, (2)(-3a)3 =-27 a3.
(3)2-2= 14，(4)a2-2a =-3a(a & lt； The correct number is (c)
1。
9. It is known that A and B are positive integers and a+b = 1998, then A+B =110.
10. If the quadratic trinomial 3x2–4x+2k can always be decomposed into the product of two linear factors in the real number range, then the value range of k is k≤ 23.
1 1. Mathematical game: It is stipulated that any real number pair (a, b) will get a new real number according to the rules: a2+b+ 1. For example, if you put (5,–1) in it, you will get 52+(–1).
12, it is known that when n= 1, a1= 0; = 0; When n=2, A2 = 2；; When n=3, a3 = 0；; ... then the value of a 1+a2+a3+a4+a5+a6 is 6.
13, decomposition coefficient:
Solution: (1) ax2-4ax+4a (2) a3–a.
= a(x2-4x+4)= a(a2– 1)
= a(x-2)2 = a(a+ 1)(a- 1)
(3) Two of 2x2+3x-6: 2x2+3x-6 = 0 are
=2(x-α)(x-β) x= -3+574，x= -3-574。
Where α and β are unary quadratic equations ∴ 2x2+3x-6.
Two of 2x2+3x-6 =0. = 2(x- -3+574 )(x- -3-574)
14, calculation: (1+x2-1x2-2x+1) ÷1x-1.
Solution: The original formula = [1+(x+1) (x-1) (x-1) 2] × (x-1).
=( 1+x+ 1x- 1)×(x- 1)
= 2xx- 1 ×(x- 1)
= 2x
15, first simplify the formula (1+1x) ÷ x2-1x2, and then please select an ideal value of x to find the value of the original formula.
Solution: (1+1x) ÷ x2-1x2 You can choose the value of x by yourself.
= x+1 x× x2 (x+1) (x-1) but x should not be 0,1and-1,otherwise.
= xx- 1 meaningless.
16, known, a >；; 0，b & lt0，c & lt0，|c| >| a | >； |b|。
Simplification: |a+b|+|a+c|-|c-b|
Solution: ∫a > 0, b<0, c<0, | c | > | a | >; |b|
∴a+b & gt； 0，a+c & lt； 0，c–b & lt； 0
∴| a+b |+| a+c |–| c-b |
= a+b-(a+c)+(c-b)
= a+b-a-c+c-b
=0
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