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)
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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