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Factorisation — Chapter Test

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Q1
a² − b² factorises as ___ ?
Difference of squares: (a + b)(a − b).
Q2
The common factor of 6x and 9 is ___ ?
The HCF of 6 and 9 is 3.
Q3
x² + 2x + 1 factorises as ___ ?
It is a perfect square: (x + 1)².
Q4
5x + 10 = 5( ? )
5(x + 2).
Q5
Factorise 6x + 9.
HCF is 3: 3(2x + 3).
Q6
Factorise x² − 9.
Difference of squares.
Q7
Factorise x² + 6x + 9.
Perfect square: (x + 3)².
Q8
Factorise x² + 5x + 6.
2 × 3 = 6 and 2 + 3 = 5.
Q9
Factorise x² − 16.
Difference of squares.
Q10
Divide 12x³ by 3x.
12 ÷ 3 = 4 and x³ ÷ x = x², so 4x².
Q11
A rectangle has area x² + 7x + 12. Its sides could be ___ ?
x² + 7x + 12 = (x + 3)(x + 4).
Q12
Factorise 8x + 12.
HCF is 4: 4(2x + 3).
Q13
Factorise x² + 7x + 10.
2 × 5 = 10 and 2 + 5 = 7.
Q14
Factorise x² − x − 6.
−3 × 2 = −6 and −3 + 2 = −1.
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