Dividing a Polynomial by a Polynomial

Q.

If $x^3+1$ is divided by $x^2+5$, then the possible degree of quotient is

1. $0$

2. $1$

3. $2$

4. None of these

Q. The value of 52 xyz (xy + yz + xz + $y^2$)(z + x) + 104xy (xy + xz + yz + $y^2$) is ___

1. $\frac{z(z+x)}{2}$
2. $\frac{z(z-x)}{2}$
3. $\frac{x(z-x)}{2}$
4. $\frac{x(z+x)}{2}$

Q.

If $x^2+y^2=47$ and $xy=\frac{19}{2}$ then what is the value of $3(x+y{)}^2+(x-y{)}^2$?

1. 170

2. 270

3. 226

4. 86

Q.

Which of the following is the expression obtained by the division of $5pq(p^2-q^2)$ by $2p(p+q)?$

1. $\frac{5q(p-q)}{4}$

2. $\frac{5q(p+q)}{2}$

3. $\frac{5q(p-q)}{2}$

4. $\frac{5q(p+q)}{4}$

Q.

For an expression to be divisible by another algebraic expression the divisor should be a factor of the dividend.

1. True

2. False

Q. If one zero of the polynomial $p\left(x\right)=(a^2+9)x^2+45x+6a$ is reciprocal of the other, find the value of a.

Q. Find the remainder when $30y^4+11y^3-42y^2+3$ is divided by $3y^2+2y$?

1. 0
2. 2y+3
3. -24y + 3
4. y-2

Q.

$2x^2+7x-1$ completely divides $10x^4+17x^3-62x^2+30x-3$ .

1. True

2. False

Q. $\text{Simplify the expression:}\frac{52wxyz(xy+yz+xz+y^2)(z+x)}{104xy(xyz+x{z}^2+y{z}^2+y^{2}z)}$

1. $\frac{w(z+x)}{2}$
2. $\frac{w(z-x)}{2}$
3. $\frac{x(z-x)}{2}$
4. $\frac{x(z+x)}{2}$

Q.

Which of the pairs given in options will add up to give $9x+5y$?

1. $3x+2y$, $2x+7y$

2. $4x+4y$, $5x+1y$

3. $3x+7y$, $6x-2y$

4. $3x+3y$, $4x+7y$

Q. What must be added to $(x^2+xy-y^2)$ to get $xy$?

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

Q.

How do you long divide $(x^2-x-12)÷(x-4)$?

Q.

Dividing $(a+b{)}^2+(a-b{)}^2$ by $(a^2+b^2)$ gives___.

Q.

The value of $(3x^2+5y^2)(4xy-5y)$, when the value of $x=1$ and $y=2$ is $-46$.

1. True

2. False

Q. 24x3−84x=

1. $8x^3-2$
2. $\frac{8x^2-2}{4}$
3. $\frac{8x^3-2}{x}$
4. $\frac{8x-2}{x}$

Q. Find the degree of the expression ${[x+(x^3-1{)}^{\frac{1}{2}}]}^5+{[x-(x^3-1{)}^{\frac{1}{2}}]}^5.$

Q.

The value of $(-3y{)}^3$ is_______.

1. (-3)³ × (y)³

2. 3(y)³

3. (-3)³ × (-y)³

4. (3)³ × (y)³

Q. Simplify the given expression:
$(3y+12b)(5a-b)÷(y+4b)(25a^2-b^2)$

1. $\frac{3}{5a+b}$
2. $\frac{5}{3a+b}$
3. $\frac{3}{5a-b}$
4. $\frac{3}{a+5b}$

Q. 5x2+8xy−4y25x−2y =

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

Q.

The value of $52xyz(xy+yz+xz+y^2)(z+x)÷104xy(xy+xz+yz+y^2)$ is:

1. $\frac{z(z+x)}{2}$

2. $\frac{z(z-x)}{2}$

3. $\frac{x(z-x)}{2}$

4. $\frac{x(z+x)}{2}$

Q.

The value of $\frac{x(x+1)(x+2)(x+3)}{x(x+1)}$ is __________.

1. (x + 2) (x + 3)

2. (x+2)

3. (x+3)

4. x(x+1)

Q.

The quotient obtained when $p{q}^2+5pq+6p$ is divided by $pq+2p$ is _______.

1. q + 3

2. q - 3

3. pq + 3p

4. q + 2

Q. ${\left(2\right)}^5\times {\left(4\right)}^5={\left(24\right)}^5$.

1. True
2. False

Q.

$Evaluate:$
$(2y+5)(2y+5)$

1. 

2. 

3. 

4. 

Q.

If we subtract $-4x^{2}y$ from $2x^{2}y$ we get:

1. -6x

2. 6

3. 6y

4. -6y

Q.

The product of $(7x-4y)$ and $(3x-7y)$ is:

1. + + 61xy

2. - - 61xy

3. + - 61xy

4. + - 37xy

Q.

What must be subtracted from $x^3-3x^2+5x-2$ to get $2x^3+x^2-4x+2$ ?

1. 

2. 

3. 

4. 

Q.

Dividing $\left(\right(a+b{)}^2+(a-b{)}^2)$ by $(a^2+b^2)$ gives

___

Q. $(x^2-4y^2)÷(x+2y)$

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

Q. 9x2+6x3x+2=

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