Factorising a Binomial

Q.

Factorise the following expression: $p^2+6p-16$

Q. Factorize : $4x^{2}y-6x^2$

1. $2x^2(2y-3)$
2. $4x(y-3)$
3. $2x^2(3y-2)$
4. $3x^2(2y-6)$

Q.

Factorize: $y^2-5y+6$

Q.

Factorise the following expression: $p^2+6p+8$

Q.

Which among the following is not a factor of $4y(y+3)$?

1. 4

2. + 3

3. None of these

4. 4( + 3)

Q. Factorize : $2x^2-18y^2$

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

Q.

Factorise:
$2xp+4xq-3yp-6yq$

1. $(p+2q)(2x-3y)$

2. $(p-2q)(2x-3y)$

3. $(p+2q)(2x+3y)$

4. $(p-2q)(2x+3y)$

Q.

The factors of $a^2+b-ab-a$ are :

1. $(a-1)(a-b)$

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

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

4. $(a+1)(a+b)$

Q. Factorize: $142a{b}^2$ and write in product form

1. $2\times 71\times a\times a\times b$
2. $2\times 71\times a\times b\times b$
3. $2\times 71\times a\times b$
4. $2\times 67\times a\times b\times b$

Q.

Find the result of the following division.
$(x^3+2x^2+3x)÷2x$

1. 1/2

2. (x²+2x+3)

3. 1

4. 1/2(x²+2x+3)

Q.

Factorise the following expression: $p^2+6p-16$

Q. Factorize : $25x^2-9$

1. $(25x+9)(25x-9)$
2. $(5x+9)(5x-9)$
3. $(5x-3)(5x-3)$
4. $(5x+3)(5x-3)$

Q.

Which among the following is not a factor of $4y(y+3)$?

1. 4

2. + 3

3. 4( + 3)

4. None of these

Q. Factorize: $161x^{2}yz$ and write in product form

1. $3\times 27\times x\times x\times y\times z$
2. $7\times 23\times x\times y\times z$
3. $7\times 23\times x\times x\times y\times z$
4. $2\times 23\times 5\times x\times x\times y\times z$

Q. Factorize : $\frac{1}{2}{a}^2-8b^2$

1. $\frac{1}{2}(a+16b)(a-16b)$
2. $\frac{1}{2}(a+4b)(a-4b)$
3. $\frac{1}{2}(a+8b)(a-8b)$
4. $\frac{1}{2}(a-4b)(a-4b)$

Q. $xy-xz+ay-az$

1. $(y-z)(x+a)$
2. $(y+z)(x+a)$
3. $(y-z)(x-a)$
4. None of these

Q.

Factorize the following expression: $6p-12q$

Q.

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

1. True

2. False

Q. $x^3{y}^2-z{x}^{2}y+x^4{y}^3=$ $\times (xy-z+x^2{y}^2)$

1. $xy$
2. $x^{2}y$
3. $x{y}^2$
4. $x^2{y}^2$

Q. $x^{2}yz+x{y}^{2}z+xy{z}^2$

1. $xyz(x-y+z)$
2. $xy(x+y+z)$
3. $xyz(x+y+z)$
4. $xz(x+y+z)$

Q. Factorise:
$p^2-3pq+2q^2$

1. $(p-2q)(p-q)$
2. $(p-q)(p-q)$
3. $(3p-2q)(p-q)$
4. $(3p-2q)(p+q)$

Q. Factorise $18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$.

1. $9x^2{y}^2(2xy-3y+4x)$
2. $9x^2{y}^2(2xy+3y+4x)$
3. $9x^2{y}^2(2xy-3y-4x)$
4. $9x^2{y}^2(2xy+3y-4x)$

Q. Factorise
$\frac{4x^2+4x+1}{x}$
[2 Marks]

Q.

Find the product of $11x{y}^{2}and-8x{y}^3$.

1. $-88x^2{y}^5$

2. $-80x^2{y}^5$

3. $-88x^3{y}^5$

4. $-80x^2{y}^4$

Q.

Which of the following is/are the factor(s)
$\text{of}4x^3+12x^2+5x+15?$

1. $(2x^2+5)$

2. $(4x^2+5)$

3. $(x+3)$

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

Q. Factorize: $210pq{r}^2$ and write in product form

1. $2\times 3\times 5\times 7\times p\times q\times r\times r$
2. $2\times 5\times 7\times p\times q\times r\times r$
3. $3\times 5\times 7\times p\times q\times r$
4. $2\times 3\times 5\times 7$

Q. The factorised form of $21x^2{y}^3+27x^3{y}^3$ is __________.

1. $3x^2{y}^3(7+9x)$
2. $7xy+9x^{2}y$
3. $7\times 3\times 4(x+y)$
4. $3x^2{y}^2(7y+9x)$

Q. Express each of the following in exponential form:
$1350$

Q. If $4qc-6td-3tc+82d$ is simplified and factorised then its factors are

1. $\left(4q-3t\right)\left(c+2d\right)$
2. $\left(4q+3t\right)\left(c-2d\right)$
3. $\left(4q-3t\right)\left(c-2d\right)$
4. $\left(4q+3t\right)\left(1+2d\right)$

Q. Factorize $x^5-x$