Division Algorithm for a Polynomial

Q.

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

$x^3-3x+1,x^5-4x^3+x^2+3x+1$
(2 marks)

Q. When $x^2-4x+11$ is divided by $x-2$, find the sum of quotient and remainder.

1. x + 2
2. x + 5
3. 2
4. x + 4

Q. $\text{If}(x-3)\text{and}(x-2)\text{are two factors of}\text{the polynomial}{x}^3-6x^2+11x-6,\text{then find the third factor.}$

1. $x-6$
2. $x-1$
3. $x-4$
4. $x-5$

Q.

In division algorithm when should one 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 A, B are correct

2. Statement B, C are correct

3. Statement C, A are correct

4. None of these

Q. When $x^4+x^3-2x^2+x+1$ is divided by $x-1$, the remainder is 2 and the quotient is q(x). Find q(x).

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

Q.

$\text{If the dividend =}{x}^4+x^3-2x^2+x+1,\text{divisor =}x-1\text{and remainder =}2,\text{then find the quotient q(x)}.$

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

2. $x^3+x^2+x$

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

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

Q.

When a polynomial is divided by (x+2), the quotient and remainder are (2x-1) and 3 respectively. Find the polynomial.

1. $2x^2+6x+11$

2. $5x^2+3x+8$

3. $6x^2+3x+9$

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

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.

Priya lost her homework paper on polynomials and she doesn't remember the divisor which, on dividing the polynomial $x^3-3x^2+x+2$ gives quotient $(x-2)$ and remainder $(-2x+4).$ Find the divisor.

1. $5x^2-7x+9$

2. $x^2-8x+7$

3. $x^2-x+1$

4. $6x^2-x+11$

Q.

What is the remainder when $3x^2-7x+5$ is divided by $(x-1)$ ?

1. 0

2. 1

3. 2

4. 3