Division of Algebraic Expressions - Exercise 8.1 | Mathematics (Maths) Class 8 PDF Download

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Question:1
Write the degree of each of the following polynomials.
i
2x
2
 + 5x
2
 - 7
ii
5x
2
 - 3x + 2
iii
2x + x
2
 - 8
iv
1
2
y
7
-12y
6
+48y
5
-10
v
3x
3
 + 1
vi
5
vii
20x
3
 + 12x
2
y
2
 - 10y
2
 + 20
Solution:
i  C o r r e c t i o n  : It is 2x
3
+5x
2
-7  instead of 2x
2
+5x
2
-7.     The degree of the polymonial  2x
3
+5x
2
-7 is 3. ii The degree of the polymonial 5x
2
-35x +2 is 2. iii The degree of the polymonial
Question:2
Which of the following expressions are not polynomials?
i
x
2
 + 2x
-2
ii
v ax +x
2
-x
3
iii
3y
3
 - v 5y
+ 9
iv
ax
1/2
 + ax + 9x
2
 + 4
v
3x
-2
 + 2x
-1
 + 4x +5
Solution:
i x
2
+2x
-2
 is not a polynomial because -2 is the power of variable x is not a non negative integer. ii v ax +x
2
-x
3
 is not a polynomial because 
1
2
 is the power of variable x is not a non
Question:3
Write each of the following polynomials in the standard form. Also, write their degree.
i
x
2
 + 3 + 6x + 5x
4
ii
a
2
 + 4 + 5a
6
iii
(x
3
 - 1)(x
3
 - 4)
iv
(y
3 
- 2)(y
3 
+ 11)
v
a
3
-
3
8
a
3
+
16
17
vi
a +
3
4
a +
4
3
Solution:
i Standard form of the given polynomial can be expressed as: 5x
4
+x
2
+6x +3 or 3 +6x +x
2
+5x
4
 The degree of the polynomial is 4. ii Standard form of the given polynomial can
   
  
   
   
 
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