LCM of Polynomials

Q. The LCM of $(x-1)(x-2)and(x-2)(x-7)$ is:

1. $(x-1)(x-2)$
2. $(x-1)(x-2)(x-7)$
3. $(x-2)(x-7)$
4. $(x-1)(x-7)$

Q. If $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$, then $\frac{x^3}{a^3}+\frac{y^3}{b^3}+\frac{z^3}{c^3}$is equal to .

1. $\frac{3xyz}{abc}$
2. $\frac{8xyz}{abc}$
3. $\frac{9xyz}{abc}$

Q.

A binomial may have degree 5

1. True

2. False

Q.

What is the LCM of $(x^2+5x+6)$ and $(x^2+7x+10)$

1. (x + 2)

2. (x + 3)

3. (x + 2)(x + 3)

4. (x + 2)(x + 3)(x + 5)

Q.

Use Euclids division algorithm to find the HCF of:

$36575,2223,1330$

Q.

Which among the following is a binomial of degree 100?

1. $100x+1$
2. $100x^2-3x+2$
3. $x^{100}-100$
4. $x^{100}-x+12$

Q.

LCM and HCF of $(x+1{)}^2$ and $x^3+1$ are ____.

1. HCF = $(x-1)$

   LCM = $(x+1)(x^2-x+1)$

2. HCF = $(x+1)$

   LCM = $(x+1)(x^2-x-1)$

3. HCF = $(x+11)$

   LCM = $(x+1)(x^2-5x+1)$

4. HCF = $(x+1)$

   LCM = $(x+1{)}^2(x^2-x+1)$

Q. Using Euclid’s division algorithm, find the HCF of 504 and 288.

1. 144
2. 72
3. 36
4. 180

Q.

Use Euclids Division Algorithm to find HCF of:

$126$ and $1078$

Q. The LCM of $(x-3)(x-5)and(x-5)(x-7)$ is:

1. $(x-3)(x-5)(x-7)$
2. $(x-3)(x-5)$
3. $(x-3)(x-7)$
4. $(x-5)(x-7)$

Q. The HCF of $3(x^2-9)(x+4)and12(x-3{)}^2$ is:

1. $3(x-3)$
2. $3(x-3)(x+4)$
3. $3(x-3)$
4. $3(x-3{)}^2$

Q.

L.C.M. of $6x^2-x-1,3x^2+7x+2and2x^2+3x-2$ is $(x+2)(2x-1)(3x+1)$

1. True

2. False

Q.

Use Euclids Division Algorithm to find HCF of:

$26565,25806,20930$

Q.

The LCM of $v^2-v$, $(v-1{)}^2$, and $v^3-1$ is

1. $v(v+1)(v-1)$ $(v^2+v+1)$

2. $v^2(v+1)(v-1)$ $(v^2+v+1)$

3. $v(v+1)(v-1)$

4. $v(v-1)$ $(v^2+v+1)$

Q.

If the polynomials $x^3+3x^2-m$ and $2x^3-mx+9$ leave the same remainder when they are divided by $(x-2)$, find the value of $m$. Also find the remainder.

1. 5, 15

2. 3, 12

3. 3, 15

4. 5, 12

Q. An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The time(in min) after which they will next make a beep together at the earliest is

Q.

LCM of $v^2-v$, $v^2-1^2$, and $v^3-1$

1. $v(v+1)(v-1)$ $(v^2+v+1)$

2. $v^2(v+1)(v-1)$ $(v^2+v+1)$

3. $v(v+1)(v-1)$

4. $v(v-1)$ $(v^2+v+1)$

Q.

Use Euclid’s Division Algorithm to show that the squares of following numbers is either of form 3m or 3m + 1 for some integer m.

253

Q.

LCM of $x^2+x-6$ and $(x-2{)}^2$ is $(x+a)$ $(x-b{)}^2$. Value of $(a+b{)}^2$ =

1. 16

2. 25

3. 36

4. 49

Q. $\text{The LCM of}(x-3{)}^2(x+4\left)\text{and}\right(x-3\left)\right(x+4{)}^2\text{is}:$

1. $(x-3{)}^2(x+4{)}^2$
2. $(x-3)(x+4{)}^2$
3. $(x-3)(x+4)$
4. $(x-3{)}^2(x+4)$

Q.

What is the LCM of $(2a+3b{)}^2$ and $(4a^2–9b^2)$

1. (2a – 3b)

2. (2a – 3b) (2a +3b) ²

3. (2a – 3b) (2a +3b)

4. (2a +3b) ²

Q. The L.C.M. of $9x^2+6x+1,3x^2+7x+2$ and $2x^2+3x-2$ is $(x+a)(2x-b)(3x+c{)}^2$. Then $a-b-c=$ .

1. 3
2. 6
3. \N
4. 9

Q. Match the expressions given on the left side with their L.C.M. given on the right side.

1. $x^2{y}^2(1-y)$
2. $18x^{2}yz$
3. $x^3$
4. $x(x-1{)}^2$

Q. The L.C.M. of $v^2-v$, $(v-1{)}^2$, and $v^3-1$ is .

1. $v^2(v-1)(v^2+v+1)$
2. $v(v-1{)}^3(v^2+v+1)$
3. $v(v-1)$
4. $v(v-1{)}^2(v^2+v+1)$

Q. The L.C.M. of $6x^2-x-1,3x^2+7x+2$ and $2x^2+3x-2$ is .

1. $(x+2)(2x-1)(3x+1)$
2. $(2x-1)(3x+1)$
3. $(2x+1)(3x-1)$
4. $(x+2)(2x+1)(3x-1)$

Q.

Use Euclid’s Division Algorithm to show that the squares of following numbers is either of form 3m or 3m + 1 for some integer m.

707

Q.

The L.C.M. of $9x^2+6x+1,3x^2+7x+2$ and $2x^2+3x-2$ is $(x+a)(2x-b)(3x+c{)}^2$. Then $a-b-c=$ _____

1. $3$

2. $6$

3. $0$

4. $9$

Q.

If $a+b=25$ and $a^2+b^2=225$, then find ab.

1. 180

2. 214

3. 204

4. 200

Q. The L.C.M. of $x^3-8$ and $x^2-5x+6$ is

1. $x-2$
2. $x^2+2x+4$
3. $(x-2)(x^2+2x+4)$
4. $(x-2)(x-3)(x^2+2x+4)$

Q. Find LCM of the following expressions :
$4a^2{b}^{2}c$ and $6a{b}^{2}d$