Page 59 - SM inner class 7.cdr

5abc – 7ab + 9ac is a trinomial in three Degree of the polynomial
variables a, b and c. The degree of the polynomial is the greatest of
x 2 the exponents (powers) of its various terms.
+ ay 6 bz is a trinomial in five variables
–
3 Let us take an example: For polynomial
2
6
5
,
a b x y and z. 2x - 3x + 5x .
,
,
4. Polynomial : An algebraic expression We observe that the above polynomial has
2
which con sists of two or more terms is called a three terms. Here the first term is 2x , the
6
5
poly no mial. second term is -3x and the third term is 5x .
Ex am ples of poly no mi als : Since, the greatest exponent is 6, the degree of
2
6
5
2a + 5b is a polynomial of two terms in two 2x - 3x +5x is also 6.
variables a and b. Therefore, the degree of the polynomial
6
2
5
2x - 3x + 5x = 6
3xy + 5x + 1 is a polynomial of three terms in
two variables x and y. Standard form of an Expression
2
3 Consider the expression 3x + 5x - 9
4
2
3
3y + 2y + 7y - 9y + x is a polynomial of
5 The degrees of first, second and third terms
five terms in two variables x and y. are 1, 2, and 0 respectively. Thus, the degrees
2
2
m + 5 mn – 7 m n + nm + 9 is a polynomial of of terms are not in the descending order.
four terms in two variables m and n. By re-arranging the terms in such a way that
2
+
3 7x 5 + 4x is a polynomial of three terms in their degrees are in descending order; we get
2
one variable x. the expression 5x + 3x - 9. Now the
2
+
3 5x 2 - 4x y + 5xy 2 is a polynomial of three expression is said to be in standard form.
terms in two variables x and y. Let us consider 3c + 6a – 2b. Degrees of all the
terms in the expression are same. Thus the
x + 5 yz 7 z +11 is a polynomial of four terms in
–
three variables x y, and z. expression is said to be already in standard
form. If we write it in alphabetical order as
+
3
1 2 + p 2 + 4 p 3 + 5p 4 + 6p 5 + 7p 6 is a 6a – 2b + 3c it looks more beautiful.
p
polynomial of seven terms in one variable p.
So, binomials, Trinomials or Others are
Polynomials.
E xercise 6.1
1. Is the fol low ing ex pres sions a poly no mial or not? If not, ex plain why.
2
+
(a) 5x + 3x - 4 (b) a 4 (c) 7 5+ (d) 3x - 2 5
2. clas si fy ing these poly no mi als by the num ber of terms:
2
(a) 5y (b) 3x - 3x + 1 (c) 5y - 10
4
2
(d) 8xy (e) 3x + x - 5x - 3x 3
3. List the terms in the fol low ing poly no mi als :
2
2
3
+
+
(a) -2x – 3x +1 (b) a + b + 2 ab (c) ax + by cz d (d) -7
4. In the given al ge braic ex pres sion; group the like and un like terms. :
2
2
2
+
(a) a - b 3 2 + b 7 2 - a 9 2 + 6 ab 5 (b) 5x y + 7xy - 3xy – 4yx 2
5. Find the de gree and con stant term of the poly no mi als.
2
2
2 3
2
4
2
2
(a) x + x 7 3 - x 2 (b) 2abc + a bc + ab c + 2acb + 7 (c) x y 2+ xy - 5 y x + 80
59
Mathematics In Focus - 7