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Class 8

Explore popular questions from Factorisation for Class 8. This collection covers Factorisation previous year Class 8 questions hand picked by experienced teachers.

Factorisation

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Q 1. Which of the following are the factor of {tex} 1 - x ^ { 2 } ? {/tex}

A

{tex} ( x + 1 ) ( x - 1 ) {/tex}

{tex} ( 1 - x ) ( 1 + x ) {/tex}

C

{tex} ( 1 - x ) ( 1 - x ) {/tex}

D

{tex} ( 1 + x ) ( x + 1 ) {/tex}

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Q 2. Which of the following is the common factor of: {tex} 5 \mathrm { xy } , 3 \mathrm { pqr } {/tex} and {tex} 40 \mathrm { xyz } ? {/tex}

A

5

B

0

C

{tex} x y {/tex}

1

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Q 3. Which of the following is quotient obtained on dividing {tex} - 18 \mathrm { xyz } ^ { 2 }{/tex} by {tex} - 3 \mathrm { xz } ? {/tex}

{tex} 6 y z {/tex}

B

{tex} - 6 y z {/tex}

C

{tex} 6 x y ^ { 2 } {/tex}

D

{tex} 6 x y {/tex}

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Q 4. Which of the following is quotient obtained on dividing {tex} \left( x ^ { 2 } - b \right) ( x - a ){/tex} by {tex} - ( x - a ) ? {/tex}

A

{tex} \left( x ^ { 2 } - b \right) {/tex}

B

{tex} \frac { - \left( x ^ { 2 } - b \right) } { ( x - a ) } {/tex}

{tex} - \left( x ^ { 2 } - b \right) {/tex}

D

{tex} - ( x + a ) {/tex}

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Q 5. Which of the following is true?

A

{tex} a b - a - b + 1 = ( 1 + a ) ( 1 - b ) {/tex}

{tex} a b - a - b + 1 = ( a - 1 ) ( b - 1 ) {/tex}

C

{tex} a b - a - b + 1 = ( 1 - a ) ( b - 1 ) {/tex}

D

{tex} a b - a - b + 1 = ( a - 1 ) ( 1 - b ) {/tex}

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Q 6. Which of the following is equal to {tex} x ^ { 3 } - 225 x {/tex}

A

{tex} x ( 1 - 15 x ) ( 1 + 15 x ) {/tex}

{tex} x ( x - 15 ) ( x + 15 ) {/tex}

C

{tex} x ( 1 - 15 x ) ( 1 - 15 x ) {/tex}

D

{tex} x ( 1 + 15 x ) ( 1 - 15 x ) {/tex}

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Q 7. Which of the following is the quotient when {tex} 44 \mathrm { x } ^ { 2 } \left( \mathrm { x } ^ { 2 } - 5 \mathrm { x } - 24 \right) {/tex} is divided by {tex} 22 \mathrm { x } ( \mathrm { x } - 8 ) {/tex}:

A

{tex} x ( x + 3 ) {/tex}

{tex} 2 x ( x + 3 ) {/tex}

C

{tex} 2 ( x - 3 ) {/tex}

D

{tex} x ( x - 3 ) {/tex}

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Q 8. By which of the following {tex} a ^ { 4 } - b ^ { 4 } {/tex} be divided to get quotient {tex} \left( a ^ { 2 } + b ^ { 2 } \right) ( a - b ) {/tex} and, remainder as 0:

A

{tex} a ^ { 2 } + b ^ { 2 } {/tex}

B

{tex} a - b {/tex}

{tex} a + b {/tex}

D

{tex} a ^ { 2 } - b ^ { 2 } {/tex}

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Q 9. Factorise : {tex} \left( 5 x - \frac { 1 } { x } \right) ^ { 2 } + 5 \left( 5 x - \frac { 1 } { x } \right) + 6 {/tex}

{tex} \left( 5 x - \frac { 1 } { x } + 3 \right) \left( 5 x - \frac { 1 } { x } + 2 \right) {/tex}

B

{tex} \left( 5 x - \frac { 1 } { x } - 3 \right) \left( 5 x - \frac { 1 } { x } - 2 \right) {/tex}

C

{tex} \left( 5 x - \frac { 1 } { x } + 3 \right) \left( 5 x - \frac { 1 } { x } - 2 \right) {/tex}

D

{tex} \left( 5 x - \frac { 1 } { x } - 3 \right) \left( 5 x - \frac { 1 } { x } + 2 \right) {/tex}

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Q 10. Factors of {tex} \left( x ^ { 3 } + \frac { 1 } { x ^ { 3 } } - 2 \right) {/tex} are:

A

{tex} \left( x + \frac { 1 } { x } + 1 \right) \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } + \frac { 1 } { x } + 1 \right) {/tex}

B

{tex} \left( x + \frac { 1 } { x } - 1 \right) \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x } + x \right) {/tex}

C

{tex} \left( x + \frac { 1 } { x } - 1 \right) \left( x ^ { 2 } + \frac { 1 } { x ^ { 2 } } - \frac { 1 } { x } + x \right) {/tex}

None of these

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Q 11. {tex} \left( \mathrm { x } ^ { 51 } - 1 \right) {/tex} is always divisible by

A

{tex} ( x + 1 ) {/tex}

{tex} ( x - 1 ) {/tex}

C

{tex} ( x + 2 ) {/tex}

D

{tex} ( x - 2 ) {/tex}

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Q 12. The factors of {tex} y ^ { 2 } + 2 + \frac { 1 } { y ^ { 2 } } {/tex} are :

{tex} \left( y + \frac { 1 } { y } \right) ^ { 2 } {/tex}

B

{tex} \left( y - \frac { 1 } { y } \right) ^ { 2 } {/tex}

C

{tex} \left( y + \frac { 1 } { y } + 1 \right) ^ { 2 } {/tex}

D

{tex} \left( y + \frac { 1 } { y } - 1 \right) ^ { 2 } {/tex}

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Q 13. When {tex} 16 x ^ { 2 } - 9 y ^ { 2 } {/tex} is resolved into factors, we get

A

{tex} ( 8 x - 3 y ) ^ { 2 } {/tex}

{tex} ( 4 x - 3 y ) ( 4 x + 3 y ) {/tex}

C

{tex} ( 4 x - 3 y ) ^ { 2 } {/tex}

D

{tex} ( 3 x - 4 y ) ( 3 x + 4 y ) {/tex}

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Q 14. The factors of {tex} y ^ { 2 } + 7 y + 10 {/tex} are

A

{tex} ( y - 5 ) ( y - 2 ) {/tex}

B

{tex} ( y - 5 ) ( y + 2 ) {/tex}

{tex} ( y + 5 ) ( y + 2 ) {/tex}

D

{tex} ( y + 5 ) ( y - 2 ) {/tex}

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Q 15. Which of the following is a common factor in {tex} 15 x ^ { 2 } {/tex} and {tex} 18 x y ^ { 2 } ? {/tex}

A

5

{tex} 3 x {/tex}

C

{tex} 5 x {/tex}

D

6

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Q 16. Which of the following is the common factor of {tex} ( 2 x - 3 ) {/tex} and {tex} ( 4 x - 6 ) ? {/tex}

A

2

B

3

{tex} 2 x - 3 {/tex}

D

{tex} 4 x - 6 {/tex}

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Q 17. {tex} 55 x y ^ { 2 } \div 11 x y = {/tex} _______

{tex} 5 y {/tex}

B

{tex} 5 x {/tex}

C

{tex} 5 x y ^ { 2 } {/tex}

D

{tex} 5 x y {/tex}

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Q 18. {tex} \frac { 5 \mathrm { x } + 10 } { 2 } = {/tex}

A

{tex} 5 x + 5 {/tex}

B

{tex} \frac { 5 x } { 2 } + 10 {/tex}

C

{tex} \frac { 5 x } { 2 } + \frac { 5 } { 2 } {/tex}

{tex} \frac { 5 x } { 2 } + 5 {/tex}

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Q 19. Which of the following is/are the factors(s) of {tex} 25 x ^ { 2 } - 36 y ^ { 2 } ? {/tex}

A

{tex} 5 x + 6 y {/tex}

B

{tex} 5 x - 6 y {/tex}

C

{tex} 25 x ^ { 2 } - 36 y ^ { 2 } {/tex}

All of these

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Q 20. {tex} a c + a d + b c + b d = {/tex}

A

{tex} ( a + b ) ( b + d ) {/tex}

B

{tex} ( a + d ) ( b + c ) {/tex}

{tex} ( a + b ) ( c + d ) {/tex}

D

None of these

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Q 21. Find the value of {tex} 9 \mathrm { x } ^ { 2 } + 3 \mathrm { x } + 1 , {/tex} when {tex} \mathrm { x } = - \frac { 1 } { 3 } {/tex}

1

B

2

C

3

D

4

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Q 22. Factorize {tex} : 4 t ^ { 4 } + 4 t ^ { 2 } + 1 {/tex}

{tex} \left( 2 t ^ { 2 } + 1 \right) ^ { 2 } {/tex}

B

{tex} ( 2 t + 2 ) ^ { 2 } {/tex}

C

{tex} \left( 2 t ^ { 2 } - 1 \right) ^ { 2 } {/tex}

D

{tex} ( 4 t + 4 ) ^ { 2 } {/tex}

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Q 23. Factorize {tex} : x ^ { 2 } y + x y ^ { 2 } + 3 x + 3 y {/tex}

{tex} ( x y + 3 ) ( x + y ) {/tex}

B

{tex} ( x y + 3 ) ( 3 x + y ) {/tex}

C

{tex} ( x + 2 y ) ( 2 x + y ) {/tex}

D

{tex} ( x y + 3 ) ( y + 3 x ) {/tex}

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Q 24. Divide {tex} x ^ { 2 } - 9 x + 14 {/tex} by {tex} x - 2 {/tex}

{tex} x - 7 {/tex}

B

{tex} x - 8 {/tex}

C

{tex} x - 5 {/tex}

D

{tex} x - 2 {/tex}

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Q 25. Divide {tex} 4 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 4 } \mathrm { r } ^ { 3 } \div 12 \mathrm { pqr } {/tex}

{tex} \frac { 1 } { 3 } \mathrm { pq } ^ { 3 } \mathrm { r } ^ { 2 } {/tex}

B

{tex} \mathrm { pqr } {/tex}

C

{tex} \mathrm { p } ^ { 2 } \mathrm { q } ^ { 3 } \mathrm { r } ^ { 2 } {/tex}

D

{tex} 3 p q ^ { 3 } r ^ { 2 } {/tex}