RD Sharma Class 8 Solutions Chapter 7 Factorization Ex 7.1

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RD Sharma Solutions for Class 8 Chapter 7 Factorization Ex 7.1 Download PDF

Find the greatest common factors (GCF / HCF) of the following polynomials : (1 – 14)

Question 1.
2x² and 12x²
Solution:
2x² and 12x²
HCF of 2 and 12 =2
HCF of x²,x²=x²
∴ HCF = 2x²

Question 2.
(6xy³ and 18x²y³
Solution:
6x³y and 18xy
HCF of 6, 18 = 6
HCF of x³ and x² = x²
HCF of y and y³ -y
∴ HCF = 6x²y

Question 3.
7x, 21x² and 14xy²
Solution:
7x, 21x² and 14xy²
HCF of 7, 21 and 14 = 7
HCF of x, x², x = x
∴ HCF = 7x

Question 4.
42x²yz and 63x³y²z³
Solution:
42x²yz and 63x³y²z³
HCF of 42 and 63 = 21
HCF of x², x³ = x²
HCF of y,y²=y
HCF of z,z³ = z
∴ HCF = 21 x²yz

Question 5.
12ax²,6a²x³ and 2a³ x⁵
Solution:
12ax², 6a²x³ and 2a³x⁵
HCF of 12, 6,2 = 2
HCF of a, a², a³ = a
HCF of x², x³, x⁵ = x²
∴ HCF = 2ax²

Question 6.
9x², 15x²y³, 6xy² and 21x²y²
Solution:
9x², 15xV, 6xy² and 21x²y²
HCF of 9, 15, 6,21 = 3
HCF of x², x², x, x² = x
HCF of 1, y³, y², y² =2
∴ HCF = 3x

Question 7.
4a²b³ -12a³b, 18a⁴b³
Solution:
4a²b³, -12a³b, 18a⁴b³
HCF of 4, 12, 18 = 2
HCF of a², a³, a⁴ = a²
HCF of b³,b, b³ = b
∴ HCF = 2a²b

Question 8.
6x²y², 9xy³, 3x³y²
Solution:
6x²y², 9xy³, 3x³y²
HCF of 6, 9, 3 = 3
HCF of x², x, x³ = x
HCF of y²,y³,y²=y²
∴ HCF = 3xy²

Question 9.
a²b³, a³b²
Solution:
a²b³, a³b²
HCF of a², a³ = a²
HCF of b³, b² = b²
∴ HCF = a²b²

Question 10.
36a²b²c⁴, 54a⁵c²,90a⁴b²c²
Solution:
36a²b²c⁴, 54a⁵c²,90a⁴b²c²
HCF of 36, 54, 90 = 18
HCF of a², a⁵, a⁴ = a²
HCF of b², 1,b²= 1
HCF of c⁴,c²,c² = c²
∴ HCF = 18a² x 1 x c² = 18a²c²

Question 11.
x³, – yx²
Solution:
x³, – yx²
HCF of x³, x² = x²
HCF of 1, y= 1
∴ HCF = x²

Question 12.
15a³, -45a², -150a
Solution:
15a³,-45a²,-150a
HCF of 15,45, 150 = 15
HCF of a³, a², a = a
∴ HCF = 15a

Question 13.
2x³y², 10x²y³, 14xy
Solution:
2x³y², 10x²y³, 14xy
HCF of 2, 10, 14 = 2
HCF of x³, x², x = x
HCF of y²,y³,y=y
∴ HCF = 2xy

Question 14.
14x³y⁵, 10x⁵y³, 2x²y²
Solution:
14x³y⁵, 10x⁵y³, 2x²y²
HCF of 14, 10, 2, = 2
HCF of x³, x⁵, x² = x²
HCF of y⁵,y³,y²=y²
∴ HCF = 2xy

Find the greatest common factor of the terms in each of the following expressions:

Question 15.
5a⁴ + 10a³ – 15a²
Solution:
5a⁴ + 10a³– 15a²
HCF of 5, 10, 15 = 5
HCF of a⁴, a³, a² = a²
∴ HCF = 5a²

Question 16.
2xyz + 3x²y + 4y²
Solution:
2xyz + 3x²y + 4y²
HCF of 2, 3,4 = 1
HCF of x, x², 1 = 1
HCF of y,y,y² =y
HCF of z, 1, 1 = 1
∴ HCF = y

Question 17.
3a²b² + 4b²c² + 12a²b²c²
Solution:
3a²b² + 4b²c² + 12a²b²c²
HCF of 3, 4, 12 = 1
HCF of a², 1, a² = 1
HCF of b², b², b² = b²
HCF of 1, c², c² = 1
∴ HCF = b²

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