Factorising into single brackets


 

Question 1: 

Factorise the following expressions:

 

1(a) 7x+21

 

ANSWER: Multiple Choice

A:  7(x+3)

B: 3(x+7)

C: 7(7+x)

D: 3(3+x)

Answer: A

Workings:

The highest common factor of 7 and 21 is 7, so this can be taken outside of the bracket and the variables divided appropriately to give 7(x+3).

Marks = 1

 

1(b) 8y-10

ANSWER: Multiple Choice

A: 2(4y -5)

B: 8(y-10)

C: 4(y-5)

D: 5(y-2)

Answer: A

Workings: 

Marks = 1

 

1(c) 7p+63

 

ANSWER: Multiple Choice

A: 7(p+9)

B: 9(p+8)

C: 8(p+7)

D: 7(p+6)

Answer: A

Workings: 

Marks = 1

 

1(d) 24m-40

ANSWER: Simple Text Answer

A: 8(3m-5)

B: 12(m+3)

C: 3(m-12)

D: 4(m-6)

Answer: A

Workings: 

Marks = 1

 

1(e) 40z+72

 

ANSWER: Simple Text Answer

A: 8(5z+9)

B: 6(12z+9)

C: 5(z+7)

D: 7(2z+9)

Answer: A

Workings: 

Marks = 1

 


 

Question 2: 

Factorise the following expressions:

 

2(a) 2x^2+12x

 

ANSWER: Multiple Choice

A: 2x(x+6)

B: x(4x+3)

C: 2x(x+10)

D: x(x+12)

Workings: 

Marks = 1

 

2(b) 5y^2+15y

ANSWER: Multiple Choice

A: 5y(y+3)

B: 5y(y+10)

C: 5y(2y+4)

D: </p> <p>Workings: [latex]

Marks = 1

 

2(c) 64m^2+10m

 

ANSWER: Simple Text Answer

 

A: 2m(32m+5)

Workings: 

Marks = 1

 

2(d) 99p^2+11p

 

ANSWER: Simple Text Answer

 

A: 11p(9p+1)

Workings: 

Marks = 1

 

2(e) 34x^2+30x

 

ANSWER: Simple Text Answer

 

A: 2x(17x+15)

Workings: 

Marks = 1

 


 

Question 3: 

Factorise the following expressions:

 

3(a) 10xy+5x

 

ANSWER: Simple Text Answer

 

A: 5x(2y+1)

Workings: 

Marks = 1

 

3(b) 12x^2 p+9x

 

ANSWER: Simple Text Answer

 

A: 3x(4xp+3)

Workings: 

Marks = 1

 

3(c) 30x^2 p+18x^2

 

ANSWER: Simple Text Answer

 

A: 6x^2 (5p+3)

Workings: 

Marks = 1

 

3(d) 50xyz+25xz

 

ANSWER: Simple Text Answer

 

A: 25xz(2y+1)

Workings: 

Marks = 1

 

3(e) 10x^2-6xy^2

 

ANSWER: Simple Text Answer

 

A: 2x(5x-3y^2)

Workings: 

Marks = 1

 

 


Question 4: 

Fully factorise the following expression.

 

4(a) 6x^2-15x

 

ANSWER: Multiple Choice (Type 1)

 

A: 3?(2?−5)

B: 3(2?^2−5?)

C:  3?^2 (2−5)

D:  6?(?−3)

 

Workings:  3?(2?−5)

Marks = 1

 

 

4(b) 8yz^2−16?^3

 

ANSWER: Multiple Choice (Type 1)

 

A: 8y(z^2  -2y)

B:  8y(z^2  -2y^2) 

C:  8y^2 (z^2  -2y^2)

D:  8yz(z -2y^2) 

 

Workings: 8y(z^2  -2y^2)

Marks = 1

 

 

4(c) 6bc^2-15b^2 c

 

ANSWER: Multiple Choice (Type 1)

 

A: 3??(3?+12?)

B:  3??(2?−5?)

C:  6??(?−9?)

D: bc(5c-14b)

 

Workings: 3bc(2c-5b)

Marks = 1

 


Question 5: 

Fully factorise the following expression.

 

5(a) 6x^2 y +9x^2– 15x

 

ANSWER: Multiple Choice (Type 1)

 

A: 3x(2xy+3x– 5)

B:  4x(2xy+5x– 5)

C:  2x(3xy-3x– 5)

D:  1x(5xy+3x– 5) 

 

Workings:  3(2x^2 y+3x^2– 5x) = 3x(2xy+3x– 5)

Marks = 2

 

5(b) 3xy^2 z -6x^2 yz^2  –9xz^2

 

ANSWER: Multiple Choice (Type 1)

 

A:   5xz(y^2-4xyz –2z)

B:  3xz(4y^2-xyz –3z)

C:   3xz(2y^2-2xyz –z)

D:  3xz(y^2-2xyz –3z)

 

Workings:  3x(y^2 z-2xyz^2–3z^2) = 3xz(y^2-2xyz –3z)

Marks = 2

 

5(c) 20b^2 c+28bc^2  -4c

 

ANSWER: Multiple Choice (Type 1)

 

A: 2c(5b^2+3bc-1)

B: 4c(6b^2-7bc-1)

C: 4c(5b^2-7bc+1)

D:  4c(5b^2+7bc-1)

 

Workings:    4(5b^2 c+7bc^2-1c) =  4c(5b^2+7bc-1)

Marks = 2