Division of a Polynomial by a Monomial

Q.

Find the remainder when $x^3+3x^2+3x+1$ is divided by $x+\mathrm{\pi }$.

Q.

Find the remainder when $x^3-a{x}^2+6x-a$ is divided by $x-a$.

Q. What will be the quotient and remainder if $(y^4+24y-10y^2)÷(y+4)$?

1. Quotient = $(y^3-4y^2+6y)$
   Remainder = 0
2. Quotient = $(y^3-4+6y)$
   Remainder = $3y$
3. Quotient = $(y^4-4y^2+6y)$
   Remainder = $3y+2$
4. Quotient = $(y^3-4y^2+6y)$
   Remainder = $3y$

Q.

Find the common factors of: $16x^3,-4x^2,32x$

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

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

Q. What is the remainder when $15p^3$ is divided by 3p?

1. 0
2. p
3. 2p
4. 1

Q.

The sum of the series $1+3x+6x^2+10x^3+.....\infty$ will be

1. $\frac{1}{{\left(1-x\right)}^2}$

2. $\frac{1}{\left(1-x\right)}$

3. $\frac{1}{{\left(1+x\right)}^2}$

4. $\frac{1}{{\left(1-x\right)}^3}$

Q.

Show that $2x+7$ is a factor of $2x^3+5x^2-11x-14$. Hence, factorize the given expression completely, using the factor theorem.

Q.

$2^{35}$divided by $5$ remainders?

Q.

Work out the following division: $(10x-25)÷(2x-5)$

Q.

Solve the following for $x$: $6a^2{x}^2-7abx-3b^2=0,a\ne 0$

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

1. Quotient = $(x^2-2x+9)$
   Remainder = $\left(17\right)$
2. Quotient = $(x^2-2x+6)$
   Remainder = $\left(17\right)$
3. Quotient = $(x^2-2x+6)$
   Remainder = $\left(17x^3\right)$
4. Quotient = $(x^3-2x^2+6)$
   Remainder = $\left(17\right)$

Q.

Carry out the following division: $\frac{28{\mathrm{x}}^4}{56\mathrm{x}}$

Q. Question 21
Find and correct the errors in the statement: $\frac{7x+5}{5}=7x$

Q.

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

1. 

2. 

3. 

4. 

Q.

Identify the remainder when $1+x+x^2+x^3+....+x^{2012}$ is divided by $x-1$

1. 2013

2. 1

3. 2012

4. 0

Q.

$\text{Divide}(a^2+7a+10)\text{by}(a+5).$

1. 1
2. $(a+1)$
3. 2
4. $(a+2)$

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

1. Quotient = $(m^2+m+2)$
   Remainder = $\left(10\right)$
2. Quotient = $(m^2+m+1)$
   Remainder = $\left(10\right)$
3. Remainder= $(m^2+m+1)$
   Quotient= $\left(10\right)$
4. Remainder= $(m^3+m+1)$
   Quotient= $(10m+2)$

Q.

Carry out the following division: $66{\mathrm{pq}}^2{\mathrm{r}}^3÷11{\mathrm{qr}}^2$

Q.

$5x^3-15x^2+25xby5x$

Q. Question 2(i)
Divide the given polynomial by the given monomial
$(5x^2-6x)÷3x$

Q. Question 2(v)
Divide the given polynomial by the given monomial
$(p^3{q}^6-p^6{q}^3)÷p^3{q}^3$

Q. Question 31

The value of $(3x^3+9x^2+27x)÷3x$ is
a) $x^2+9+27x$
b) $3x^3+3x^2+27x$
c) $3x^3+9x^2+9$
d) $x^2+3x+9$

Q. What will be the quotient and remainder if $(3x-3x^2-12+x^4+x^3)÷(2+x^2)$?

1. Quotient = $(x^3+2x-5)$
   Remainder = $(x-1)$
2. Quotient = $(x^2+4x-5)$
   Remainder = $(7x-2)$
3. Quotient = $(x^2+x-5)$
   Remainder = $(x-2)$
4. Remainder= $(x^2+x-5)$
   Quotient= $(x-2)$

Q.

Dividing $2x^2+13x+15$ by $x+5$ and then substituting $x=2$ in the resulting expression gives

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Q. Question 5
$\frac{3t-2}{4}-\frac{2t+3}{3}=\frac{2}{3}-t$

Q.

Divide:
(i) $5m^3-30m^2+45m$ by $5m$
(ii) $8x^2{y}^2-6x{y}^2+10x^2{y}^3$ by $2xy$
(iii) $9x^{2}y-6xy+12x{y}^2$ by $-3xy$
(iv) $12x^4+8x^3-6x^2$ by $-2x^2$

Q. Find the value of ‘t’ for which the polynomial, $p\left(x\right)=x^3+3x^2+2x+t$ gives 3 as remainder when divided by $(x–1)$.

1. -2
2. -3
3. -4
4. -5

Q. Question 30

The value of $(2x^2+4)÷2$ is
a) $2x^2+2$
b) $x^2+2$
c) $x^2+4$
d) $2x^2+4$

Q. Question 2(iii)
Divide the given polynomial by the given monomial
$8(x^3{y}^2{z}^2+x^2{y}^3{z}^2+x^2{y}^2{z}^3)÷4x^2{y}^2{z}^2$