3a. Pedagogy of Mathematics (Part II) - Algebra (Ex 3.1)
1. PEDAGOGY OF
MATHEMATICS – PART II
By
Dr. I. Uma Maheswari
Principal
Peniel Rural College of Education,Vemparali, Dindigul District
iuma_maheswari@yahoo.co.in
35. Given Expression Is it a
polynomial?
Reason
(i) (1 / x
2
) + 3x – 4 = x
-2
+ 3x – 4 No Negative integral power
(ii) x
2
(x – 1) Yes Positive integral power
(iii) (1 / x) (x + 5) = x
-1
* (x + 5)
= x
-1+1
* 5x
-1
= x
0
+ 5x
-1
No One of the integral powers is
negative.
(iv) (1 / x
-2
) + ( 1 / x
-1
) + 7 = x
2
+ x + 7 Yes Positive integral power
(v) √5 x
2
+ √3 x + √2 Yes Positive integral power
(vi) m
2
– ∛m + 7m – 10
= m
2
– m
1/3
+ 7m – 10
No One of the powers is fractional.
Solution:
36.
37. Given Expression Coefficient of x
2
Coefficient of x
(i) 4 + (2 / 5)x
2
– 3x 2 / 5 -3
(ii) 6 – 2x
2
+ 3x
3
– √7 x -2 – √7
(iii) πx
2
– x + 2 π -1
(iv) √3 x
2
+ √2x + 0.5 √3 √2
(v) x
2
– (7 / 2)x + 8 1 – (7 / 2)
Solution:
38.
39. Given Expression Degree of the polynomial
(i) 1 – √2y
2
+ y
7
7
(ii) (x
3
– x
4
+ 6x
6
) / x
2
4
(iii) x
3
(x
2
+ x) 5
(iv) 3x
4
+ 9x
2
+ 27x
6
6
(v) 2√5p
4
– (8p
3
/ √3) + (2p
2
/ 7) 4
Solution:
40.
41. Given Expression Standard form of the expression
(i) x – 9 + √7x
3
+ 6x
2
√7x
3
+ 6x
2
+ x – 9
(ii) √2x
2
– (7 / 2)x
4
+ x – 5x
3
– (7 / 2)x
4
– 5x
3
+ √2x
2
+ x
(iii) 7x
3
– (6 / 5)x
2
+ 4x – 1 7x
3
– (6 / 5)x
2
+ 4x – 1
(iv) y
2
– √5y
3
– 11 – (7 / 3) y + 9y
4
9y
4
– √5y
3
+ y
2
– (7 / 3) y – 11
Solution:
50. Solution:
In order to find the total amount paid by him, multiply the cost of 1 chocolate by the number of
chocolates he buys.
Cost of 1 chocolate = x + y
Number of chocolates that Amir buys = x + y
Total amount = (x + y) (x + y)
= (x + y)2 —(1)
= x2 + 2xy + y2
By applying the values of x and y,
= (10 + 5)2
= 152
= 225
Hence, he has to pay Rs. 225.
51. Solution:
Length of the rectangle = 3x + 2
Breadth of the rectangle = 3x – 2
Area of rectangle = (3x + 2)(3x – 2)
= 9x2 – 6x + 6x – 4
= 9x2 – 4
If x = 20
Area of rectangle = 9(20)2 – 4
= 9(400) – 4
= 3600 – 4
= 3596
52. Solution:
The degree of the polynomial p(x) is 1.
Degree of the polynomial q(x) is 2.
The product of polynomials is 3.
Hence it is a cubic polynomial.