Exercise 7.1
Page-7.3Question 1:
Find the greatest common factor (GCF/HCF) of the following polynomial:
2x2 and 12x2
Answer 1:
The numerical coefficients of the given monomials are 2 and 12. So, the greatest common factor of 2 and 12 is 2.
The common literal appearing in the given monomials is x.
The smallest power of x in the two monomials is 2.
The monomial of the common literals with the smallest powers is x2.
Hence, the greatest common factor is 2x2.
Question 2:
Find the greatest common factor (GCF/HCF) of the following polynomial:
6x3y and 18x2y3
Answer 2:
The numerical coefficients of the given monomials are 6 and 18. The greatest common factor of 6 and 18 is 6.
The common literals appearing in the two monomials are x and y.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The monomial of the common literals with the smallest powers is x2y.
Hence, the greatest common factor is 6x2y.
Question 3:
Find the greatest common factor (GCF/HCF) of the following polynomial:
7x, 21x2 and 14xy2
Answer 3:
The numerical coefficients of the given monomials are 7, 21 and 14. The greatest common factor of 7, 21 and 14 is 7.
The common literal appearing in the three monomials is x.
The smallest power of x in the three monomials is 1.
The monomial of the common literals with the smallest powers is x.
Hence, the greatest common factor is 7x.
Question 4:
Find the greatest common factor (GCF/HCF) of the following polynomial:
42x2yz and 63x3y2z3
Answer 4:
The numerical coefficients of the given monomials are 42 and 63. The greatest common factor of 42 and 63 is 21.
The common literals appearing in the two monomials are x, y and z.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The smallest power of z in the two monomials is 1.
The monomial of the common literals with the smallest powers is x2yz.
Hence, the greatest common factor is 21x2yz.
Question 5:
Find the greatest common factor (GCF/HCF) of the following polynomial:
12ax2, 6a2x3 and 2a3x5
Answer 5:
The numerical coefficients of the given monomials are 12, 6 and 2. The greatest common factor of 12, 6 and 2 is 2.
The common literals appearing in the three monomials are a and x.
The smallest power of a in the three monomials is 1.
The smallest power of x in the three monomials is 2.
The monomial of common literals with the smallest powers is ax2.
Hence, the greatest common factor is 2ax2.
Question 6:
Find the greatest common factor (GCF/HCF) of the following polynomial:
9x2, 15x2y3, 6xy2 and 21x2y2
Answer 6:
The numerical coefficients of the given monomials are 9, 15, 6 and 21. The greatest common factor of 9, 15, 6 and 21 is 3.
The common literal appearing in the three monomials is x.
The smallest power of x in the four monomials is 1.
The monomial of common literals with the smallest powers is x.
Hence, the greatest common factor is 3x.
Question 7:
Find the greatest common factor (GCF/HCF) of the following polynomial:
4a2b3, −12a3b, 18a4b3
Answer 7:
The numerical coefficients of the given monomials are 4, -12 and 18. The greatest common factor of 4, -12 and 18 is 2.
The common literals appearing in the three monomials are a and b.
The smallest power of a in the three monomials is 2.
The smallest power of b in the three monomials is 1.
The monomial of the common literals with the smallest powers is a2b.
Hence, the greatest common factor is 2a2b.
Question 8:
Find the greatest common factor (GCF/HCF) of the following polynomial:
6x2y2, 9xy3, 3x3y2
Answer 8:
The numerical coefficients of the given monomials are 6, 9 and 3. The greatest common factor of 6, 9 and 3 is 3.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 2.
The monomial of common literals with the smallest powers is xy2.
Hence, the greatest common factor is 3xy2.
Question 9:
Find the greatest common factor (GCF/HCF) of the following polynomial:
a2b3, a3b2
Answer 9:
The common literals appearing in the three monomials are a and b.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 2.
The monomial of common literals with the smallest powers is a2b2.
Hence, the greatest common factor is a2b2.
Question 10:
Find the greatest common factor (GCF/HCF) of the following polynomial:
36a2b2c4, 54a5c2, 90a4b2c2
Answer 10:
The numerical coefficients of the given monomials are 36, 54 and 90. The greatest common factor of 36, 54 and 90 is 18.
The common literals appearing in the three monomials are a and c.
The smallest power of a in the three monomials is 2.
The smallest power of c in the three monomials is 2.
The monomial of common literals with the smallest powers is a2c2.
Hence, the greatest common factor is 18a2c2.
Question 11:
Find the greatest common factor (GCF/HCF) of the following polynomial:
x3, − yx2
Answer 11:
The common literal appearing in the two monomials is x.
The smallest power of x in both the monomials is 2.
Hence, the greatest common factor is x2.
Question 12:
Find the greatest common factor (GCF/HCF) of the following polynomial:
15a3, − 45a2, − 150a
Answer 12:
The numerical coefficients of the given monomials are 15, -45 and -150. The greatest common factor of 15, -45 and -150 is 15.
The common literal appearing in the three monomials is a.
The smallest power of a in the three monomials is 1.
Hence, the greatest common factor is 15a.
Question 13:
Find the greatest common factor (GCF/HCF) of the following polynomial:
2x3y2, 10x2y3, 14xy
Answer 13:
The numerical coefficients of the given monomials are 2, 10 and 14. The greatest common factor of 2, 10 and 14 is 2.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is xy.
Hence, the greatest common factor is 2xy.
Question 14:
Find the greatest common factor (GCF/HCF) of the following polynomial:
14x3y5, 10x5y3, 2x2y2
Answer 14:
The numerical coefficients of the given monomials are 14, 10 and 2. The greatest common factor of 14, 10 and 2 is 2.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 2.
The smallest power of y in the three monomials is 2.
The monomial of common literals with the smallest powers is x2y2.
Hence, the greatest common factor is 2x2y2.
Question 15:
Find the greatest common factor of the terms in each of the following expression:
5a4 + 10a3 − 15a2
Answer 15:
Terms are expressions separated by plus or minus signs. Here, the terms are 5a4, 10a3 and 15a2.
The numerical coefficients of the given monomials are 5, 10 and 15. The greatest common factor of 5, 10 and 15 is 5.
The common literal appearing in the three monomials is a.
The smallest power of a in the three monomials is 2.
The monomial of common literals with the smallest powers is a2.
Hence, the greatest common factor is 5a2.
Question 16:
Find the greatest common factor of the terms in each of the following expression:
2xyz + 3x2y + 4y2
Answer 16:
The expression has three monomials: 2xyz, 3x2y and 4y2.
The numerical coefficients of the given monomials are 2, 3 and 4. The greatest common factor of 2, 3 and 4 is 1.
The common literal appearing in the three monomials is y.
The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is y.
Hence, the greatest common factor is y.
Question 17:
Find the greatest common factor of the terms in each of the following expression:
3a2b2 + 4b2c2 + 12a2b2c2
Answer 17:
The expression has three monomials: 3a2b2, 4b2c2 and 12a2b2c2.
The numerical coefficients of the given monomials are 3, 4 and 12. The greatest common factor of 3, 4 and 12 is 1.
The common literal appearing in the three monomials is b.
The smallest power of b in the three monomials is 2.
The monomial of common literals with the smallest powers is b2.
Hence, the greatest common factor is b2.
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