Division of a Polynomial by a Polynomial

Q. Simplify the given expression:
$(3y+12b)(5a-b)÷(y+4b)(25a^2-b^2)$

1. $\frac{3}{5a+b}$
2. $\frac{5}{3a+b}$
3. $\frac{3}{5a-b}$
4. $\frac{3}{a+5b}$

Q. $\text{Simplify the expression:}\frac{52wxyz(xy+yz+xz+y^2)(z+x)}{104xy(xyz+x{z}^2+y{z}^2+y^{2}z)}$

1. $\frac{w(z+x)}{2}$
2. $\frac{w(z-x)}{2}$
3. $\frac{x(z-x)}{2}$
4. $\frac{x(z+x)}{2}$

Q. Divide $(6ab-b^2+12ac-2bc)by(6a-b)$.

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

Q.

For an expression to be divisible by another algebraic expression the divisor should be a factor of the dividend.

1. True

2. False

Q. Find the remainder when $30y^4+11y^3-42y^2+3$ is divided by $3y^2+2y$?

1. 2y+3
2. -24y + 3
3. y-2
4. 0

Q.

If a + b + c = 12 and $a^2+b^2+c^2=50$; find ab + bc + ca

1. x(x+1)

2. (x+3)

3. (x+2)

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

Q.

Dividing $\left(\right(a+b{)}^2+(a-b{)}^2)$ by $(a^2+b^2)$ gives ___

Q.

Dividing $x(3x^2-27)$ by $3(x-3)$ gives $x^2+3x$.

1. x+3

2. x²+3x

Q. Carry out the following division.
$9x^2{y}^2(3z-24)÷27xy(z-8)$

Q.

Which of the following is the expression obtained by the division of $5pq(p^2-q^2)$ by $2p(p+q)?$

1. $\frac{5q(p-q)}{4}$

2. $\frac{5q(p+q)}{2}$

3. $\frac{5q(p-q)}{2}$

4. $\frac{5q(p+q)}{4}$