Introduction to Factorization

Q.

Express as the product of three factors.

(e) $385=\_\_\_\_\_\_\_\_$

Q.

How to find the factors of $1800$?

Q.

What are two different factor trees for $60$?

Q.

How do you factor the expression $x^2+5x-6$?

Q.

The factors of ($x^4-625)$ are

1. $(x^2–25),(x^2+25)$

2. $(x^2+25)$

3. $(x^2-10x+25)$, $(x^2+5x+25)$

4. Do not exist.

Q.

The number of prime numbers among the numbers $105!+2,105!+3,105!+4,...105!+104,105!+105$ is

1. $31$

2. $32$

3. $33$

4. None of these

Q.

Factorise: $2x^2-3x+1$

Q.

What is the complex conjugate of $7-8i$?

Q.

Which of the following cannot be a factor of any positive integer?

1. 0

2. 1

3. The number itself.

4. 2

Q.

Find the factors of the following number :

$324$

Q.

Find whether $12$ is a factor of $288$.

Q.

Find the factors of $388$.

Q.

State whether true or false:

$4x^2$is a factor of $4x(x+3)$.

1. True

2. False

Q.

Factorising $m^2$ + 7m - 60 and dividing it by (m - 5) gives ___________ .

1. 4(m-6)

2. (m+12)

3. None of these

4. 2(m+6)

Q.

Write all the factors of $72$ ?

Q. Factorize: $3-a(4+7a)$

1. $(a+1)(7a-3)$
2. $(a-1)(3-7a)$
3. $(a-1)(7a-3)$
4. $(a+1)(3-7a)$

Q. What are the factors of $x^2+5x+6$?

1. x + 3
2. x + 2
3. x - 3
4. x + 5

Q. Factorize: $3a^2-9ab$

1. $3a(3a-3b)$
2. $3a(a-3b)$
3. $3b(3a-3)$
4. $3a(a-9b)$

Q.

Factorise $a^2-81(b-c{)}^2$

1. (a+ 9b+9c)(a-9b-9c)

2. (a-b+c)(a-b-c)

3. (a+ 9b- 9c)(a-9b-9c)

4. (a+ 81b- 81c)(a-81b-81c)

Q. Which of the following expressions are factorizable ?

1. $x^2-3x-54$
2. $x(2x-1)-1$
3. $3x^2+4x-10$
4. $2x^2+2x-75$

Q.

Divide $3x^3-2x^2+5$ by $x^2-1$

1. $\frac{3x+4}{x^2-1}$

2. 3x + $\frac{3x+4}{x^2-1}$

3. 3x - 2 + $\frac{3x+4}{x^2-1}$

4. 3x - 2 + $\frac{3x+4}{x-1}$

Q. When we factorize $x^2+3x+2$ , ____ is one of the factors.

1. x + 3
2. x - 1
3. x + 1
4. x - 2

Q.

If $x^3+a{x}^2+bx+6$ has $x-2$ as a factor and leaves a remainder 3 when divided by $x-3$. Find the values of a and b.

1. a = 3 and b = 1

2. a = -3 and b = 1

3. a = -3 and b = -1

4. a = 3 and b = -1

Q. is not the factor of 18.

1. 3
2. 6
3. 7
4. 9

Q. is not a factor of $x^3-x$.

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

Q. Factorize the following expressions :
(i) ${(5x-\frac{1}{x})}^2+4(5x-\frac{1}{x})+4,x\ne 0$

(ii) $36x^2-12x+1-25y^2$

(iii) $x^4+x^2+1$

(3 marks)

Q. The number 7 has only two factor, 1 and 7.

1. False
2. True

Q. Factorize: $a^2+4b^2-3a+6b-4ab$

1. $(a-b)(a+2b-3)$
2. $(a-2b)(a-2b-3)$
3. $(2a-b)(a-b-3)$
4. $(a-2b)(a-b-3)$

Q.

Find all possible factors of $729$ ?

Q.

List all the factors of $100$.