Division of a Polynomial by a Binomial

Q.

Why is division by 0 not defined?

Q. What will be the quotient and remainder if $(6x^4+3x^2-9+5x+5x^3)÷(x^2-1)$?

1. Quotient = $(6x^4+5x+9)$
   Remainder = $(10x^2+1)$
2. Remainder= $(6x^2+5x+9)$
   Quotient= $\left(10x\right)$
3. Quotient = $(6x^4+5x+9)$
   Remainder = $\left(10x\right)$
4. Quotient = $(6x^4+5x+9)$
   Remainder = $(x+1)$

Q. What will be the quotient and remainder if $(a^4-a^3+a^2-a+1)÷(a^3-2)$?

1. Quotient = $(a-1+a^4)$
   Remainder = $(a^2+a-11)$
2. Quotient = $(a+51)$
   Remainder = $(a^4+a-1)$
3. Quotient = $(a-1)$
   Remainder = $(a^2+a-1)$
4. Quotient = $(a^2-1)$
   Remainder = $(2a^2+a-1)$

Q.

In division algorithm when should we stop the division process?
1. When the remainder is zero.
2. When the degree of the remainder is less than the degree of the divisor.
3. When the degree of the quotient is less than the degree of the divisor.

1. Statement 1, 2 are correct

2. Statement 2, 3 are correct

3. Statement 3, 1 are correct

4. None of these

Q. Why division by zero is not possible?

Q.

When we divide $3t^4+5t^3-7t^2+2t+2$ by $t^2+3t+1$, we get $3t^2-4t+2$ as quotient.

1. True

2. False

Q. What will be the quotient and remainder if $(a^4-a^3+a^2-a+1)÷(a^3-2)$?

Q.

$If{x}^2+y^2=14andxy=3,findthevalueof2{(x+y)}^2-5{(x-y)}^2$.

1. 0

2. 106

3. 14

4. 52

Q.

Divide $x^5-4x^3+x^2+3x+6$ by $x^3-3x+1$, and then find the remainder and quotient.

1. 7,

2. 8,

3. 7,

4. 8,

Q. The quotient obtained when $15x^6-9x^4+x^3+6x+12$ is divided by $3x^2$ is

1. $5x^4-3x^2$
2. $5x^3+3x^2$
3. $5x^4+3x^2$
4. $5x^3-3x^2$

Q. The quotient obtained when $100b^7$ is divided by $25b^7$ is

1. $4b$
2. $4$
3. $4b^2$
4. $\frac{4}{b}$

Q.

The degree of the polynomial obtained when $8-6x+x^2-7x^3+x^5$ is subtracted from$x^4-6x^3+x^2-3x+1$ is

1. 5

2. 1

3. 3

4. 4

Q. What will be the quotient and remainder if $6x^4+3x^2-9+5x+5x^3÷(x^2-1)$?

1. Quotient = $(6x^2+5x+9)$
   Remainder = $\left(10x\right)$
2. Quotient = $(6+5x+9x)$
   Remainder = $\left(10x^3\right)$
3. Remainder= $(6x^2+5x+9)$
   Quotient = $\left(10x\right)$
4. Remainder= $(6x^2+5x+9)$
   Quotient = $\left(10x^2\right)$

Q. $4x^2$ completely divides $8x^6-12x^3$.

1. True
2. False

Q. Find the sum of quotient and remainder on dividing $28$$x^3$ by $3$$x^2$.
(2 marks)

Q. Remainder for $\frac{-13x^2+4x^3+2x-7}{x^2+3x-2}$

1. $4x-25$
2. $4x-25+\frac{85x-57}{x^2+3x-2}$
3. $\frac{85x-57}{x^2+3x-2}$
4. $85x-57$

Q. What will be the quotient and remainder if $(6x^3+8x^2)÷2x$ ?

1. Remainder= $3x^2+4x^3$
   Quotient= $12x$
2. Quotient = $3x+4$
   Remainder = 0
3. Remainder= $3x^2+4x^3$
   Quotient= 0
4. Quotient = $3x^2+4x$
   Remainder = 0

Q. Match the following polynomials with their respective quotients when divided by $x$.

1. $3x^3-2$
2. $5x+7x^2$
3. $8$
4. $-6x^5+10x^3$

Q. State True or False.

1. True
2. False

Q. The quotient obtained when $4m^5-4m^3+4$ is divided by $2m^2$ is

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

Q.

When we divide $3t^4+5t^3-7t^2+2t+2$ by $t^2+3t+1$, we get $3t^2-4t+2$.

1. 

2. 

Q. Divide: $\frac{3x^3-2x^2+6}{x^2-1}$

1. $3x-2-\frac{3x+4}{x^2-1}$
2. $3x-2+\frac{3x+4}{3x}$
3. $3x-2+\frac{3x+4}{x^2-1}$
4. $3x+4+\frac{3x-2}{x^2-1}$

Q. Find the GCD of the polynomials $x^4+3x^3-x-3$ and $x^3+x^2-5x+3$.

Q. The quotient obtained when $x^3-3x^2+x+2$ is divided by $x-2$ is .

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

Q. What is the remainder when $6x^4+5x^3+3x^2+5x-9$ is divided by $x^2-1$ ?

1. 5x
2. 10
3. 10x
4. 3x

Q.

Divide $x^3-125$ by $x^2+5x+25$ and find the quotient.

1. x + 5

2. x - 5

3. 

4. x + 2

Q.

If we divide a number by its factor, there can be a remainder left over.

1. True
2. False

Q.

The expression obtained by multiplying $(7x-4x^2+2x^3-5)$ with $(3x-2)$ is:

1. $6x^4-16x^3+29x^2-x+1$

2. $6x^4-16x^3+27x^2-x+10$

3. $5x^4-16x^3+29x^2-x+10$

4. $6x^4-16x^3+29x^2-29x+10$

Q. The quotient $q\left(x\right)$ is when the polynomial $(x^4+x^3-2x^2+x-1)$ is divided by $(x-1)$.

1. $x^3+2x^2+1$
2. $x^3-2x^2+2$
3. $3x^3+2x^2+1$
4. $x^3+6x^2+1$

Q. What is the quotient of $\frac{x^3+3x^2-4x-12}{x^2+x-6}$ ?

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