    ### Answers − Factorising quadratics of the form x2 + bx + c

#### 1.   Factorise x2 + 6x + 8

Here b = 6 and c = 8.
The factors of c = 8 are (1, 8) and (2, 4)
Out of the above factors choose (2, 4) as it satisfies the conditions:

 n + q = b n × q = c 2 + 4 = 6 2 × 4 = 8

So the factors are (x + 2)(x + 4)

To check work in the opposite direction:

#### 2.   Factorise x2 + 9x + 18

Here b = 9 and c = 18.
The factors of c = 18 are (1, 18), (2, 9) and (3, 6)
Out of the above factors choose (3, 6) as it satisfies the conditions:

 n + q = b n × q = c 3 + 6 = 9 3 × 6 = 18

So the factors are (x + 3)(x + 6)

To check work in the opposite direction:

#### 3.   Factorise x2 + x − 56

 Here b = 1 and c = − 56. The factors of c = 56 are (1, 56), (2, 28), (4, 14) and (7, 8) Out of the above factors choose (7, 8) as it satisfies the conditions:
 n − q = b n × −q=−c n > q 8 − 7 = 1 8 × −7=−56 8 > 7

So the factors are (x + 8)(x − 7)

To verify work in the opposite direction:

#### 4.   Factorise x2 + 10x − 24

 Here b = 10 and c = − 24. The factors of c = 24 are (1, 24), (2, 12), (3, 8) and (4, 6) Out of the above factors choose (2, 12) as it satisfies the conditions:
 n − q=b n × −q=−c n > q 12 − 2=10 12 × −2=−24 12>2

So the factors are (x + 12)(x − 2)

To verify work in the opposite direction:

#### 5.   Factorise x2 − 16x + 60

 Here b = − 16 and c = 60. The factors of c = 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12) and (6, 10) Out of the above factors choose (6, 10) as it satisfies the conditions:
 −n − q = −b −n × −q = c −6 − 10 = −16 −6 × −10 = 60

So the factors are (x − 6)(x − 10)

To check work in the opposite direction:

#### 6.   Factorise x2 − 15x + 36

 Here b = − 15 and c = 36. The factors of c = 36 are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6) Out of the above factors choose (3, 12) as it satisfies the conditions:
 −n − q = −b −n × −q = c −3 − 12 = −15 −3 × −12 = 36

So the factors are (x − 3)(x − 12)

To check work in the opposite direction:

#### 7.   Factorise x2 − 8x − 48

 Here b = − 8 and c = − 48. The factors of c = 48 are (1, 48), (2, 24), (3, 16), (4, 12) and (6, 8) Out of the above factors choose (4, 12) as it satisfies the conditions:
 n − q=−b n × −q=−c q > n 4 −12=−8 4 × −12=−48 12>4

So the factors are (x + 4)(x − 12)

To verify work in the opposite direction: back to:   