Factorisation by Common Factors

Q.

Factorize by splitting the middle term:

1. 

2. 

3. 

4. 

Q. The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is:
___

Q.

Factorise:$64m^3–343n^3$.

Q.

Factorise the following expression: $6xy-4y+6-9x$

Q. Question 1(i)
Find the common factors of the given terms.
$12x,36$

Q. Question 1(iii)
Find the common factors of the terms
$14pq,28p^2{q}^2$

Q. Question 2(vii)
Factorise the following expressions
$10a^2-15b^2+20c^2$

Q.

If $y=\frac{\left(a+b{x}^{{\displaystyle \frac{3}{2}}}\right)}{x^{{\displaystyle \frac{5}{4}}}}$and $y^{}=0$ at $x=5$. Then the ratio of $a:b$is ?

1. $5:2$

2. $\surd 5:1$

3. $1:2$

4. $3:5$

Q.

Find $7÷3.5$.

Q.

Using quadratic formula solve for $x$:

$36x^2-12ax+(a^2-b^2)=0$

Q.

Factorise the following expression: $a{x}^2+bx$

Q. WHAT IS THE HCF OF SMALLEST PRIME NUMBER AND SMALLEST COMPOSITE NUMBER

Q.

In which table does $49$come?

Q. Divide $44(x^4-5x^3-24x^2)$ by $11x(x-8)$. [4 MARKS]

Q. Factorise: a²-1+2b-b²​​​​

Q.

Factorise $2x^2-7x+6$

1. (2x-2)(2x-3)

2. (x-2)(2x-1)

3. (x-2)(2x-3)

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

Q. Question 1(v)
Find the common factors of the terms
$6abc,24a{b}^2,12a^{2}b$

Q.

Factorize: $x^2-10x+21$.

Q. Question 2(ix)
Factorise the following expressions
$x^{2}yz+x{y}^{2}z+xy{z}^2$

Q.

Find the common factors of:$10pq,20qr,20rp$

Q.

Factorise the following expressions.

(i) a² + 8a + 16

(ii) p² − 10p + 25

(iii) 25m² + 30m + 9

(iv) 49y² + 84yz + 36z²

(v) 4x² − 8x + 4

(vi) 121b² − 88bc + 16c²

(vii) (l + m)² − 4lm (Hint: Expand (l + m)² first)

(viii) a⁴ + 2a²b² + b⁴

Q.

What is the difference between the remainder theorem and the factor theorem?

Q.

Factorize the following :

3x - 9

Q.

Factorize each of the following algebraic expressions.

(2x - 3y) (a + b) + (3x - 2y) (a + b)

Q.

$\left\{x\in R:\frac{2x-1}{x^3+4x^2+3x}\right\}$ is equal to:

1. $R-\left\{0\right\}$

2. $R-\left\{0,1,3\right\}$

3. $R-\left\{0,-1,-3\right\}$

4. $R-\left\{0,-1,-3,\frac{1}{2}\right\}$

Q.

Question 111 (i)

What will happen to the volume of the cube, if its edge is tripled?

Q. Question 88 (iii)

Factorise the following expression.

$a{x}^3-b{x}^2+cx$

Q.

Factorise :

$63a^2{b}^2-7$

Q.

Factorize the following $1-64a^3-12a+48a^2$.

Q. Question 1(ii)
Find the common factors of the given terms.
$2y,22xy$