Division of polynomials

Q. Explain remainder theorem with an example.

Q. The remainder obtained when a polynomial f(x) is divided by (x+a) is equal to f(-a).

1. True
2. False

Q. What will be the remainder when a polynomial $q\left(x\right)$ of degree n (n>1) is divided by a polynomial $p\left(x\right)=x-a$ which is a factor of $q\left(x\right)$ ?

1. 1
2. a
3. x + a
4. 0

Q. A polynomial can be formed with any number of variables.

1. True
2. False

Q. The remainder obtained when a polynomial f(x) is divided by (x+a) is equal to f(-a).

1. True
2. False

Q. The remainder obtained when a polynomial f(x) is divided by (x+a) is equal to f(-a).

1. True
2. False

Q. ‘$x^{-2}+3$’ is a polynomial.

1. True
2. False

Q.

$\text{Given the area of rectangle is}A=25a^2-35a+69.\text{The length is given}\text{as}(5a-3).\text{Find the width of the}\text{rectangle.}$

1. $5a-3$

2. $5a-4$

3. $4a-5$

4. $a-4$

Q. Find the remainder on dividing the polynomial $(x^3-3x^2+5x+7)$ by $(x-3)$. Is $(x-3)$ a factor of this polynomial? Why?

Q.

Statement1: The polynomial $P\left(x\right)=4x^3–3x^2+5x–6$ when divided by $x–1$ gives zero as the remainder.

Statement2: $(x–1)$ is a factor of the polynomial $P\left(x\right)=4x^3–3x^2+5x–6$.

1. Both the statements are true; and statement 2 is the correct explanation of statement 1.
2. Both the statements are true; and statement 2 is not the correct explanation of statement 1.
3. Statement 1 is true and statement 2 is false.
4. Statement 1 is false and statement 2 is true.

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. The degree of zero polynomial is .

1. \N
2. 1
3. undefined