问题1.确定下列各表达式的项及其系数：
(i)7x 2 yz – 5xy
(ii)x 2 + x + 1
(iii)3x 2 y 2 – 5x 2 y 2 z 2 + z 2
(iv)9 – ab + bc – ca
(v)a / 2 + b / 2 – ab
(vi)0.2x – 0.3xy + 0.5y
解决方案：
(i) 7x2yz – 5xy
In this expression there are two terms:
7x2yz and – 5xy
The coefficient of 7x2yz is 7
The coefficient of –5xy is –5
(ii) x2 + x + 1
In this expression there are three terms:
x2, x and 1
The coefficient of x2 is 1
The coefficient of x is 1
The coefficient of 1 is 1
(iii) 3x2y2 – 5x2y2z2 + z2
In this expression there are three terms:
3x2y, -5x2y2z2 and z2
The coefficient of 3x2y is 3
The coefficient of -5x2y2z2 is -5
The coefficient of z2 is 1
(iv) 9 – ab + bc – ca
In this expression there are four terms:
9, -ab, bc and -ca
The coefficient of 9 is 9
The coefficient of -ab is -1
The coefficient of bc is 1
The coefficient of -ca is -1
(v) a/2 + b/2 – ab
In this expression there are three terms:
a/2, b/2, and -ab
The coefficient of a/2 is 1/2
The coefficient of b/2 is 1/2
The coefficient of -ab is -1
(vi) 0.2x – 0.3xy + 0.5y
In this expression there are three terms:
0.2x, -0.3xy and 0.5y
The coefficient of 0.2x is 0.2
The coefficient of -0.3xy is -0.3
The coefficient of 0.5y is 0.5
问题2.将以下多项式分类为单项式，二项式和三项式。哪些多项式不适合任何类别?
(i)x + y
(ii)1000
(iii)x + x 2 + x 3 + x 4
(iv)7 + a + 5b
(v)2b – 3b 2
(vi)2y – 3y 2 + 4y 3
(vii)5倍– 4年+ 3倍
(viii)4a – 15a 2
(ix)xy + yz + zt + tx
[x)pqr
(xi)p 2 q + pq 2
(xii)2p + 2q
解决方案：
(i) x + y
The given expression contains two terms x and y
∴ It is Binomial
(ii) 1000
The given expression contains one term 1000
∴ It is Monomial
(iii) x + x2 + x3 + x4
The given expression contains four terms
∴ It belongs to none of the categories
(iv) 7 + a + 5b
The given expression contains three terms
∴ It is Trinomial
(v) 2b – 3b2
The given expression contains two terms
∴ It is Binomial
(vi) 2y – 3y2 + 4y3
The given expression contains three terms
∴ It is Trinomial
(vii) 5x – 4y + 3x
The given expression contains three terms
∴ It is Trinomial
(viii) 4a – 15a2
The given expression contains two terms
∴ It is Binomial
(ix) xy + yz + zt + tx
The given expression contains four terms
∴ It belongs to none of the categories
(x) pqr
The given expression contains one term
∴ It is Monomial
(xi) p2q + pq2
The given expression contains two terms
∴ It is Binomial
(xii) 2p + 2q
The given expression contains two terms
∴ It is Binomial