HCF & LCM of Polynomials
Click the appropriate answer:
1 HCF stands for
Highest common factor Lowest common factor Highest common factor
2 LCM can also be written as
Greatest common multiple Lowest common division Lowest common multiple
3 HCF and LCM can be found by
Squaring method Division method Substraction
4 L.C.M X G.C.D =
Square of polynomials product of polynomials Sum of polynomials
5 The two metods of finding HCF are
Multiplication and squaring Completing squares and additions Factorisation and succesive division
6 Sometimes polynomials can not be resolved into
Numbers Factors Alphabets
7 In the method of successive divisions the first step is
arranging polynomials in descending powers adding the polynomials seperating the polynomials
8 LCM can be found out with the help of following 2 methods
Division & Multiplication Addition & Subtraction Factorisation and with help of HCF
9 Product of GCD and LCM = mxn if m and n are
odd numbers natural numbers even numbers
10 The process of finding HCF and LCM of positive integers and also of polynomials
can not be defined differ exactly same
11 The HCF of 27x2 and 36x is
9x 3x2 12x
12 The HCF of 48x2 and 56x is
7x2 8x 6x
13 The HCF of 13x2and 18x3 is
6x2 12x 3x2
14 If (x-a) is the divisior of x2-4x+3 and x2+3x-3 then a2-4a+3 and a2+3a-3 is equal to
1 Zero -1
15 Common factor of any two monomials is the
LCM of the monomials Multiple of one monomial HCF of the monomial
16 The HCF of (x2-4) and -(4-x2) is
(x-2) (x+2) (x+2) (x-2)2
17 The HCF of two polynomials is
Highest numerator of them Highest common divisor of them. Highest multiple of them None
18 If the HCF of x2-2x-24 and x2-ax-6 is x-6 then the value of a is
2 10 5
19 If the HCF of x2-zx-2 and x2-3x+2 is ( x-2 ) then the value of z is
1 0 -1
20 The division of m2-m-8 is (m-a) so
(m-a)2 =8 (m-a) =8 a2-a-8=0
21 The LCM of 4x2 and 6x is
4x 12x2 3x2
22 Find c if x-1 is a factor of x2+cx+1
1 2 -2
23 Find the LCM of x2+3x+2 and (x-1)
(x-1)(x-2) (x+1)2 (x+2)(x-1)
24 Find the LCM of x(x-1)(x+1)2 and x2(x-1)2(x+1)
x(x-1)(x+1) (x+1)x x2(x-1)2(x+1)2
25 Find the LCM of x2-1 and x4+2x2-3
(x2-1)(x2+3) (x-1)(x+3) (x+3)2
26 The GCD of two polynomials (x4+x+1) and (x2+1) is
2 1 -2
27 x+1 is the factor of
2x2-x-2 x2-1 3x2+5x+6
28 The LCM of 96x2y3z4 and 32x2yz2 is
96x4y3z4 132xyz3 16x3yz3
29 The HCF of two polynomials is x2(x-a) and their LCM is 36x3(x+a) (x3-a3). If one of the polynomials is 4x2(x2-a2) the other is
(x-a)2(x+a) 9x(x2+xa+a2) (x+a)(x-a)3
30 The HCF of two polynomials is x2+x+1 and their LCM is x4+x2+1. If one of them is x2+x+1 then the other is
x2+1 x3-x2+1 x4+x2+1