Abhishek Chauhan and Vivek Singhal Solutions for Chapter: Factorisation, Exercise 3: Topic Exercise 14.3

If the division of the following algebraic expression is $3x^{k}y$ then find $k$.

$51x^3{y}^{2}z÷17xyz$

If division of the following algebraic expression is $\frac{4x{z}^k}{y}$ then find $k$.

$76x^{3}y{z}^3÷19x^2{y}^2$

Divide the following algebraic expression:

${(x}^2+2x+1)÷\left(x+1\right)$

Divide the following algebraic expression:

${(49x}^2-36y^2)÷(7x+6y)$

Divide the given polynomial by the given monomial.

$9p^{2}q(3r-21)÷3rpq$

Solve the following algebraic expression by factorisation:

$[2p\left(m-n\right)+q\left(n-m\right)]÷(2p-q)$

Solve the following algebraic expression by factorisation:

$\left[\right(x-y{)}^2+\left(x-y\right)]÷(x-y+1)$

Factories the following expressions and divide them.

$\left[\left(m^2+10m+25\right)-256\right]÷\left(m+21\right)$