Division of Polynomials using Factorization

Q. Find the quotient when $x^3+x^2+x+1$ is divided by $x+1$.

1. $x+1$
2. $x^2+1$
3. $x-1$
4. $x^2-1$

Q. Divide $(a^{2}bc+a{b}^{2}c+ab{c}^2)$ by $5abc$.

1. $\frac{(a+b+c)}{5}$
   
2. $5(a+b+c)$
3. $\frac{(a+b+c)}{5abc}$
   
4. $\frac{abc(a+b+c)}{5}$
   

Q. Find the degree of the quotient when $4x^3{y}^4{z}^5$ is divided by $16x^2{y}^2{z}^2$.

1. $12$
2. $6$
3. $4$
4. $\frac{1}{4}$
   

Q. Divide $x^3+7x^2+12x$ by $x^2+3x$.

1. $x^2+3$
2. $x^2+4$
3. $x+3$
4. $x+4$

Q. The quotient on dividing a polynomial $4d^2+8d+16d^4$ by a monomial $4d^2$ is

1. A polynomial
2. Not a polynomial
3. $4d^2+1+2d^{-1}$
4. Both (b) and (c).