Factors of Algebraic Expression

Q.

Explain why 7×6×5×4×3×2×1+5 is a composite number.

Q.

Factorise the term $a^2+bc+ab+ac$

1. $(a+b^2)(a+c).$

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

3. $(a^2+b)(a+c).$

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

Q.

what is factorial?

Q. What are the common factors in 3xy and 9yz?

1. 1, 3, y
2. x, y, z
3. 3, 9, x, y, z
4. 3, y

Q. Express 15abc as the product of its factors.

1. 15 × a × bc
2. 3 × 5 × a × b × c
3. 15 × a × b × c
4. 5 × 3 × abc

Q. Express each of the following as a product of prime factors only in exponential form: 54?36

Q. Use the formula to find the factors.

(2) m² – 25

Q.

The product 108 x 144 expressed as product of prime factors is

1. 3⁷ x 2⁶

2. 2⁸ x 3⁵

3. 2⁶ x 3⁵

4. 2⁵ x 3⁶

Q. Use the formula to find the factors.

(5) 36r² – 1

Q.

$\text{Which of the following are the factors of}12ab+9a+12+16b?$

1. $(3a-4)\text{and}(4b-3)$

2. $(3a-4)\text{and}(4b+3)$

3. $(3a+4)\text{and}(4b+3)$
4. $(3a+4)(4b-3)$

Q.

express the following as product of prime factors only in exponential form 192x 729

Q.

Rename the number in expanded form using exponents:

78093

850000

154034

3400600

Q.

The product 108 x 144 expressed as product of prime factors is

1. 3⁷ x 2⁶

2. 2⁸ x 3⁵

3. 2⁵ x 3⁶

4. 2⁶ x 3⁵

Q. 1 is a factor of every number.

1. False
2. True

Q. Number of factors of 12 are

1. 1
2. 5
3. 12
4. 6

Q.

Using suitable algebraic identity, find the value of ${\left(4.9\right)}^2$.

1. 24.01
2. 24
3. 25
4. 24.25

Q. Use the formula to find the factors.

(12) $1-\frac{36m^2}{49n^2}$

Q. Use the formula to find the factors.

(10) $\frac{r^2}{s^2}-\frac{81}{100}$

Q. The expression $x^9-x$ has:

1. 5 factors
2. 4 factors
3. 2 factors
4. 3 factors

Q.

Factorise the expression:
$a{x}^2+b{y}^2+bxy+axy$

1. $(x+y)(ax+by)$

2. $(x-y)(ax-by)$

3. $(x+y)(ax-by)$

4. $(ax+by)(ax+by)$

Q.

Select the factors of $a^2+7a+10$

1. $(a+2)$

2. $(a+4)$

3. $(a+3)$

4. $(a+5)$

Q. Which of the following represents the factorisation of
$26x{y}^2.$

1. $26\times x{y}^2$
2. $26x\times y^2$
3. $26\times x\times y^2$
4. $2\times 13\times x\times y\times y$

Q. Write the factors of the following monomials:

(1) 7p
(2) 6m
(3) 9xy
(4) 22ab
(5) p²q
(6) 10xy²
(7) 5a²
(8) 15m²n
(9) 30a²b²
(10) 12x²

Q. Use the formula to find the factors.

(11) $\frac{16}{25}-\frac{y^2}{x^2}$

Q. Use the formula to find the factors.

(6) 121 – 49n²