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Textbook | NCERT |

Class | Class 8 |

Subject | Maths |

Chapter | Chapter 7 |

Chapter Name | Factorization |

Exercise | Ex 7.1 |

**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 1.2x ^{2} and 12x^{2}Solution:**2x

^{2}and 12x

^{2}HCF of 2 and 12 =2

HCF of x

^{2},x

^{2}=x

^{2}∴ HCF = 2x

^{2}

**Question 2.**

**(6xy**

^{3}and 18x^{2}y^{3}**Solution:**

6x

^{3}y and 18xy

HCF of 6, 18 = 6

HCF of x

^{3}and x

^{2}= x

^{2}HCF of y and y

^{3}-y

∴ HCF = 6x

^{2}y

**Question 3.7x, 21x ^{2} and 14xy^{2}Solution:**7x, 21x

^{2}and 14xy

^{2}HCF of 7, 21 and 14 = 7

HCF of x, x

^{2}, x = x

∴ HCF = 7x

**Question 4.**

**42x**

^{2}yz and 63x^{3}y^{2}z^{3}**Solution:**

42x

^{2}yz and 63x

^{3}y

^{2}z

^{3}HCF of 42 and 63 = 21

HCF of x

^{2}, x

^{3}= x

^{2}HCF of y,y

^{2}=y

HCF of z,z

^{3}= z

∴ HCF = 21 x

^{2}yz

**Question 5.12ax ^{2},6a^{2}x^{3} and 2a^{3 }x^{5}**

**Solution:**

12ax

^{2}, 6a

^{2}x

^{3}and 2a

^{3}x

^{5}HCF of 12, 6,2 = 2

HCF of a, a

^{2}, a

^{3}= a

HCF of x

^{2}, x

^{3}, x

^{5}= x

^{2}∴ HCF = 2ax

^{2}

**Question 6.**

**9x**

^{2}, 15x^{2}y^{3}, 6xy^{2}and 21x^{2}y^{2}**Solution:**

9x

^{2}, 15xV, 6xy

^{2}and 21x

^{2}y

^{2}HCF of 9, 15, 6,21 = 3

HCF of x

^{2}, x

^{2}, x, x

^{2}= x

HCF of 1, y

^{3}, y

^{2}, y

^{2}=2

∴ HCF = 3x

**Question 7.**

**4a**

^{2}b^{3}-12a^{3}b, 18a^{4}b^{3}**Solution:**

4a

^{2}b

^{3}, -12a

^{3}b, 18a

^{4}b

^{3}HCF of 4, 12, 18 = 2

HCF of a

^{2}, a

^{3}, a

^{4}= a

^{2}HCF of b

^{3},b, b

^{3}= b

∴ HCF = 2a

^{2}b

**Question 8.6x ^{2}y^{2}, 9xy^{3}, 3x^{3}y^{2}**

**Solution:**

6x

^{2}y

^{2}, 9xy

^{3}, 3x

^{3}y

^{2}

HCF of 6, 9, 3 = 3

HCF of x

^{2}, x, x

^{3}= x

HCF of y

^{2},y

^{3},y

^{2}=y

^{2}∴ HCF = 3xy

^{2}

**Question 9.**

**a**

^{2}b^{3}, a^{3}b^{2}**Solution:**

a

^{2}b

^{3}, a

^{3}b

^{2}HCF of a

^{2}, a

^{3}= a

^{2}HCF of b

^{3}, b

^{2}= b

^{2}∴ HCF = a

^{2}b

^{2}

**Question 10.**

**36a**

^{2}b^{2}c^{4}, 54a^{5}c^{2},90a^{4}b^{2}c^{2}**Solution:**

36a

^{2}b

^{2}c

^{4}, 54a

^{5}c

^{2},90a

^{4}b

^{2}c

^{2}HCF of 36, 54, 90 = 18

HCF of a

^{2}, a

^{5}, a

^{4}= a

^{2}HCF of b

^{2}, 1,b

^{2}= 1

HCF of c

^{4},c

^{2},c

^{2}= c

^{2}∴ HCF = 18a

^{2}x 1 x c

^{2}= 18a

^{2}c

^{2}

**Question 11.x ^{3}, – yx^{2}Solution:**x

^{3}, – yx

^{2}HCF of x

^{3}, x

^{2}= x

^{2}HCF of 1, y= 1

∴ HCF = x

^{2}

**Question 12.**

**15a**

^{3}, -45a^{2}, -150a**Solution:**

15a

^{3},-45a

^{2},-150a

HCF of 15,45, 150 = 15

HCF of a

^{3}, a

^{2}, a = a

∴ HCF = 15a

**Question 13.**

**2x**

^{3}y^{2}, 10x^{2}y^{3}, 14xy**Solution:**

2x

^{3}y

^{2}, 10x

^{2}y

^{3}, 14xy

HCF of 2, 10, 14 = 2

HCF of x

^{3}, x

^{2}, x = x

HCF of y

^{2},y

^{3},y=y

∴ HCF = 2xy

**Question 14.**

**14x**

^{3}y^{5}, 10x^{5}y^{3}, 2x^{2}y^{2}**Solution:**

14x

^{3}y

^{5}, 10x

^{5}y

^{3}, 2x

^{2}y

^{2}

HCF of 14, 10, 2, = 2

HCF of x

^{3}, x

^{5}, x

^{2}= x

^{2}HCF of y

^{5},y

^{3},y

^{2}=y

^{2}∴ HCF = 2xy

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

**Question 15.5a ^{4} + 10a^{3} – 15a^{2}Solution:**5a

^{4}+ 10a

^{3}– 15a

^{2}HCF of 5, 10, 15 = 5

HCF of a

^{4}, a

^{3}, a

^{2}= a

^{2}∴ HCF = 5a

^{2}

**Question 16.**

**2xyz + 3x**

^{2}y + 4y^{2}**Solution:**

2xyz + 3x

^{2}y + 4y

^{2}HCF of 2, 3,4 = 1

HCF of x, x

^{2}, 1 = 1

HCF of y,y,y

^{2}=y

HCF of z, 1, 1 = 1

∴ HCF = y

**Question 17.3a ^{2}b^{2} + 4b^{2}c^{2} + 12a^{2}b^{2}c^{2}Solution:**

3a

^{2}b

^{2}+ 4b

^{2}c

^{2}+ 12a

^{2}b

^{2}c

^{2}HCF of 3, 4, 12 = 1

HCF of a

^{2}, 1, a

^{2}= 1

HCF of b

^{2}, b

^{2}, b

^{2}= b

^{2}HCF of 1, c

^{2}, c

^{2}= 1

∴ HCF = b

^{2}

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