RS Aggarwal Class 9 Math Chapter 2 Polynomials Exercise 2G Solution

EXERCISE 2G

Question 1:
x² + 11x + 30
= x² + 6x + 5x + 30
= x (x + 6) + 5 (x + 6)
= (x + 6) (x + 5).

Question 2:
x² + 18x + 32
= x² + 16x + 2x + 32
= x (x + 16) + 2 (x + 16)
= (x + 16) (x + 2).

Question 3:
x² + 7x – 18
= x² + 9x – 2x – 18
= x (x + 9) – 2 (x + 9)
= (x + 9) (x – 2).

Question 4:
x² + 5x – 6
= x² + 6x – x – 6
= x (x + 6) – 1 (x+ 6)
= (x + 6) (x – 1).

Question 5:
y² – 4y + 3
= y² – 3y – y + 3
= y (y – 3) – 1 (y – 3)
= (y – 3) (y – 1).

Question 6:
x² – 21x + 108
= x² – 12x – 9x + 108
= x (x – 12) – 9 (x – 12)
= (x – 12) (x – 9).

Question 7:
x² – 11x – 80
= x² – 16x + 5x – 80
= x (x – 16) + 5 (x – 16)
= (x – 16) (x + 5).

Question 8:
x² – x – 156
= x² – 13x + 12x – 156
= x (x – 13) + 12 (x – 13)
= (x – 13) (x + 12).

Question 9:
z² – 32z – 105
= z² – 35z + 3z – 105
= z (z – 35) + 3 (z – 35)
= (z – 35) (z + 3)

Question 10:
40 + 3x – x²
= 40 + 8x – 5x – x²
= 8 (5 + x) -x (5 + x)
= (5 + x) (8 – x).

Question 11:
6 – x – x²
= 6 + 2x – 3x – x²
= 2(3 + x) – x (3 + x)
= (3 + x) (2 – x).

Question 12:
7x² + 49x + 84
= 7(x² + 7x + 12)
= 7 [x² + 4x + 3x + 12]
= 7 [x (x + 4) + 3 (x + 4)]
= 7 (x + 4) (x + 3).

Question 13:
m² + 17mn – 84n²
= m² + 21mn – 4mn – 84n²
= m (m + 21n) – 4n (m + 21n)
= (m + 21n) (m – 4n).

Question 14:
5x² + 16x + 3
= 5x² + 15x + x + 3
= 5x (x + 3) + 1 (x + 3)
= (5x + 1) (x + 3).

Question 15:
6x² + 17x + 12
= 6x² + 9x + 8x + 12
= 3x (2x + 3) + 4(2x + 3)
= (2x + 3) (3x + 4).

Question 16:
9x² + 18x + 8
= 9x² + 12x + 6x + 8
= 3x (3x+ 4) +2 (3x + 4)
= (3x + 4) (3x + 2).

Question 17:
14x² + 9x + 1
= 14x² + 7x + 2x + 1
= 7x (2x + 1) + (2x + 1)
= (7x + 1) (2x + 1).

Question 18:
2x² + 3x – 90
= 2x² – 12x + 15x – 90
= 2x (x – 6) + 15 (x – 6)
= (x – 6) (2x + 15).

Question 19:
2x² + 11x – 21
= 2x² + 14x – 3x – 21
= 2x (x + 7) – 3 (x + 7)
= (x + 7) (2x – 3).

Question 20:
3x² – 14x + 8
= 3x² – 12x – 2x +8
= 3x (x – 4) – 2(x – 4)
= (x – 4) (3x – 2).

Question 21:
18x² + 3x – 10
= 18x² – 12x + 15x – 10
= 6x (3x – 2) + 5 (3x – 2)
= (6x + 5) (3x – 2).

Question 22:
15x² + 2x – 8
= 15x² – 10x + 12x – 8
= 5x (3x – 2) + 4 (3x – 2)
= (3x – 2) (5x + 4).

Question 23:
6x² + 11x – 10
= 6x² + 15x – 4x – 10
= 3x (2x + 5) – 2(2x+ 5)
= (2x + 5) (3x – 2).

Question 24:
30x² + 7x – 15
= 30x² – 18x + 25x – 15
= 6x (5x – 3) + 5 (5x- 3)
= (5x – 3) (6x + 5).

Question 25:
24x² – 41x + 12
= 24x² – 32x – 9x + 12
= 8x (3x – 4) – 3 (3x – 4)
= (3x – 4) (8x – 3).

Question 26:
2x² – 7x – 15
= 2x² – 10x + 3x – 15
= 2x (x – 5) + 3 (x – 5)
= (x – 5) (2x + 3).

Question 27:
6x² – 5x – 21
= 6x² + 9x – 14x – 21
= 3x (2x + 3) – 7 (2x + 3)
= (3x – 7) (2x + 3).

Question 28:
10x² – 9x – 7
= 10x² + 5x – 14x – 7
= 5x (2x + 1) – 7 (2x+ 1)
= (2x + 1) (5x – 7).

Question 29:
5x² – 16x – 21
= 5x² + 5x – 21x – 21
= 5x (x + 1) -21 (x + 1)
= (x + 1) (5x – 21).

Question 30:
2x² – x – 21
= 2x² + 6x – 7x – 21
= 2x (x + 3) – 7 (x + 3)
= (x + 3) (2x – 7).

Question 31:
15x² – x – 28
= 15x² + 20x – 21x – 28
= 5x (3x + 4) – 7 (3x + 4)
= (3x + 4) (5x – 7).

Question 32:
8a² – 27ab + 9b²
= 8a² – 24ab – 3ab + 9b²
= 8a (a – 3b) – 3b (a – 3b)
= (a – 3b) (8a – 3b).

Question 33:
5x² + 33xy – 14y²
= 5x² + 35xy – 2xy – 14y²
= 5x (x + 7y) – 2y (x + 7y)
= (x + 7y) (5x – 2y).

Question 34:
3x³ – x² – 10x
= x (3x² – x – 10)
= x [3x² – 6x + 5x – 10]
= x [3x (x – 2) + 5 (x – 2)]
= x (x – 2) (3x + 5).

Question 35:

Question 36:

Question 37:

Question 38:

Question 39:

Question 40:

Question 41:

Question 42:

Question 43:

Question 44:

Question 45:
Let x + y = z
Then, 2 (x + y)² – 9 (x + y) – 5

Now, replacing z by (x + y), we get

Question 46:
Let 2a – b = c
Then, 9 (2a – b)² – 4 (2a – b) -13

Now, replacing c by (2a – b) , we get
9 (2a – b)² – 4 (2a – b) – 13

Question 47:
Let x – 2y = z
Then, 7 (x – 2y)² – 25 (x – 2y) + 12

Now replace z by (x – 2y), we get
7 (x – 2y)² – 25 (x – 2y) + 12

Question 48:
Let x² = y
Then, 4x⁴ + 7x² – 2

Now replacing y by x², we get