Factors of natural numbers

Q.

What is the meaning of the consecutive composite number​?

Q.

If a number x is divided by 95, then remainder is 30. If the same no x is divided by 5, then what is the remainder.

Q.

Show that x-1 is a factor of x³-1

Q. Find the value of ''a" so that 1-7x is a factor of -14x³-47x²-14x+a. Do it in Dickson method.

Q.

___ is used to find the HCF of given set of two polynomials.

1. Division algorithm

2. Multiplication algorithm

3. Addition algorithm

4. Subtraction algorithm

Q.

If one of the factor of x² – 2x + 1 is (x -1) then its second factor is:

1. (x - 1)

2. (x - 2)

3. (2x + 1)

4. (x + 1)

Q.

State the following as prime or composite: $23$

Q.

Which among the following are not twin primes?

1. $3,5$

2. $5,7$

3. $7,9$

4. $11,13$

Q. Let P(x) be (x2 – 5x + k) and Q(x) be (x3 – 4x2 – 5x + m). If (x – 2) and (x – 3) are respectively the factor of P(x) and Q(x), then degree of Q(x)/P(x) is (1) 3 (2) 2 (3) 1 (4) Not defined

Q.

If one factor of x² + 7x + 10 is (x + 2) then the other factor is:

1. (x - 5)

2. (x + 5)

3. (x + 4)

4. (x + 3)

Q.

If AB is divisible by 5 but not divisible by 2 and BA is divisible 3. Then which of the following is the possible values of A and B?

1. (x-2)(x-5)= – 7x + 10

2. (x+2) (x-2) = - 4

3. A = 7, B = 5
4. A = 4, B = 0

Q. Without actual division, show that (x³ − 3x² − 13x + 15) is exactly divisible by (x² + 2x − 3).

Q. If (x¹⁰⁰ + 2x⁹⁹ + k) is divisible by (x + 1), then the value of k is
(a) 1
(b) 2
(c) −2
(d) −3

Q. An irreducible factor is a factor which cannot be expressed further as a of factors.

1. Product
2. Addition
3. Subtraction

Q.

Find the value of 'a' such that (x-1) is the factor of x² + ax +9.

1. a = 9

2. a = -10

3. a = -9

4. a = 10

Q.

Identify the term whose irreducible factor form is:

-11 x p x p x p x q x q x q x q x r x r

1. -11p³q⁴

2. -11p²q³r¹

3. 11p³q⁴r²

4. -11p³q⁴r²

Q.

23 is a factor of 23.

1. True

2. False

Q.

Write any pair of twin prime.

Q.

If AB is divisible by 5 but not divisible by 2 and BA is divisible 3. Then which of the following is possible value of A and B?

1. (x-2)(x-5)= – 7x + 10

2. (x+2) (x-2) = - 4

3. A=7, B=5
4. A=4, B=0

Q.

If AB is divisible by 5 but not divisible by 2 and BA is divisible 3. Then which of the following is possible value of A and B?

1. (x-2)(x-5)= – 7x + 10

2. (x+2) (x-2) = - 4

3. A=7, B=5
4. A=4, B=0

Q. If f(x) = x³ + x² − ax + b is divisible by x² − x write the value of a and b.

Q. 12 can be expressed as:

1. $3\times 2\times 2$
2. $2\times 2\times 2$
3. $4\times 2\times 2$
4. $3\times 3\times 2$

Q.

An irreducible factor is a factor which cannot be expressed further as a ___ of factors.

Q.

An irreducible factor is a factor which cannot be expressed further as a ___ of factors.

Q.

Write all the factors of the following number.

$27$

Q. Without actual division, prove that 2x⁴ − 6x³ + 3x² + 3x − 2 is exactly divisible by x² − 3x + 2.

Q. 6 has three factors.

1. True
2. False

Q. 6 has three factors.

1. True
2. False

Q.

Q.

The numbers with more than two factors are called ________.

1. prime

2. composite

3. natural
4. integer