Division of an Expression by a Monomial

Q.

Divide $7x^2+14x$ by $(x+2).$

1. $4x$

2. $5x$

3. $7x$

4. $6x$

Q.

Divide -15x³y²z⁴ by 5xyz.

1. 3x²yz

2. -3x²yz³

3. 5xyz

4. 3x²yz³

Q.

The GCD of m²-3m-18 and m²+5m+6 is:

1. m-6

2. m+3

3. 1

4. m+6

Q. Divide using factorization: { (a) (a^{12+a^6b^6+b^{12) by (a^6-a^3b^3+b^6) { (b) (x^8-y^3) by (x^3+xy^2+x^2y+y^3)

Q. $\text{Divide}(m^2+7m-60)\text{by}(m+12).$

1. 4(m-6)
2. 2(m+6)
3. (m-5)
4. (m-12)

Q. $\text{Divide}(10a^{3}b-14a{b}^3)\text{by}ab.$

1. $(5a^2-7b^2)$
2. $2(5a^2-7b^2)$
3. $2(7a^2-5b^2)$
4. $2(5a^2+7b^2)$

Q. The number of pages in each book are 7a${}^3$ + 8b. If the total number of pages in all books are 14a${}^4$ + 16ab, how many books are there?

1. 2
2. 2b
3. 2a
4. a

Q.

Divide the given polynomial by the given monomial.

(i) (5x² − 6x) ÷ 3x

(ii) (3y⁸ − 4y⁶ + 5y⁴) ÷ y⁴

(iii) 8(x³y²z² + x²y³z² + x²y²z³) ÷ 4x²y²z²

(iv) (x³ + 2x² + 3x) ÷ 2x

(v) (p³q⁶ − p⁶q³) ÷ p³q³

Q. $\text{Divide}(8m^3+9m^2+10m)\text{by}2m.$

1. $4m^2+\frac{9}{2}m+5$
2. $4m^3+\frac{9}{2}{m}^2+5m$
3. $4m^2+\frac{9}{2}m+10$
4. $4m^3+\frac{9}{2}m+5$

Q.

The value of$(-27{\mathrm{x}}^2\mathrm{y})÷(–9\mathrm{xy})$ is

1. $3\mathrm{xy}$

2. $-3\mathrm{xy}$

3. $-3x$

4. $3x$

Q. Divide the binomial by the monomial. Write the quotient and the remainder.

(6) 18b⁴ + 13b³; 2b²

Q. Which of the following is the quotient obtained by dividing (6md + 3mc + 9me) by 3m?

1. d + c + e
2. 2d + c + 3e
3. d + 2c + 3e
4. 2d + 3c + 4e

Q. Simplify the expression:
$(2x^3+4)÷2$

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

Q. Divide:
(i) 24x²y³ by 3xy
(ii) 36xyz² by −9xz
(iii) −72x²y²z by −12xyz
(iv) −56mnp² by 7mnp

Q.

What should be multiplied with 20x²y³ to get 40x⁴y⁵?

1. x²y²

2. 20x²y²

3. 4²y²

4. 2x²y²

Q. Divide the polynomial by the binomial. Write your answer in the form: Dividend = divisor × quotient + remainder

(4) b⁴ – 12b²; b² + 1

Q. Divide 3x³y² + 2x²y + 15xy by 3xy.

Q. $\frac{6x^4+18x^3-3x^2}{3x^2}$ =

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

Q. If $y=2$, then the value of $\frac{(xy+2x)}{x}$ will be

1. 1
2. 2
3. 3
4. 4

Q. Divide:
(a² + 2ab + b²) − (a² + 2ac + c²) by 2a + b + c

Q. Divide the first polynomial by the second. Explain the steps.

(1) 21b; 7
(2) 36p²; 6p
(3) 5a³; a³
(4) −30n²; 3n
(5) 15m³; 5m
(6) 2b⁵; b²
(7) 28x⁴; −7x²
(8) −8y⁵; y³

Q. Divide the binomial by the monomial. Write the quotient and the remainder.

(7) 24m⁴ – 16m²; 8m²

Q.

How can I divide ((root of 5)x⁴) by 5x³?

Q. Divide 5x³ − 15x² + 25x by 5x.

Q. Divide 6x³y²z² by 3x²yz.

Q. Divide the binomial by the monomial. Write the quotient and the remainder.

(7) 24m⁴ – 16m²; 8m

Q. Divide (5a³ − 4a² + 3a + 18) by (a² − 2a + 3).

Q. $\text{Divide}(10a^{3}b-14a{b}^3)\text{by}ab.$

1. $(5a^2-7b^2)$
2. $2(5a^2-7b^2)$
3. $2(7a^2-5b^2)$
4. $2(5a^2+7b^2)$

Q.

While dividing a polynomial by a monomial, ​ we divide each term of the polynomial in the numerator by the monomial in the denominator.

1. True
2. False

Q. If $y=3$, then find the value of $\frac{(xy+2x)}{x}$.

1. 5