    ### Answers − Factorising quadratics of the form ax2 + bx + c, where a is not equal to 1

#### 1.   Factorise 2x2 + 10x + 8

Here a = 2, b = 10 and c = 8

 i. Possible factors of a: (2, 1) ii. Possible factors of c: (4, 2) and (8, 1) iii. Work out the x term. As c is positive, select two factors of a and c that total to b.

Factor of a with first factor of c:

 iv. As c is postive the signs of the factors are the same as b:(2x + 2)(x + 4)

 v. To check work in the opposite direction:

#### 2.   Factorise 3x2 + 21x + 18

Here a = 3, b = 21 and c = 18

 i. Possible factors of a: (3, 1) ii. Possible factors of c: (6, 3), (9, 2) and (18, 1) iii. Work out the x term. As c is positive, select two factors of a and c that total to b.

Factor of a with first factor of c:

 iv. As c is postive the signs of the factors are the same as b:(3x + 3)(x + 6)

 v. To check work in the opposite direction:

#### 3.   Factorise 4x2 + 20x − 24

Here a = 4, b = 20 and c = −24

 i. Possible factors of a: (4, 1) and (2, 2) ii. Possible factors of c: (6, 4), (8, 3), (12, 2) and (24, 1) iii. Work out the x term. As c is negative, select two factors of a and c that differ by b.

First factor of a with first factor of c:

 iv. As c is negative the signs of the factors are different:

 v. To check work in the opposite direction:

#### 4.   Factorise 2x2 + 9x − 56

Here a = 2, b = 9 and c = −56

 i. Possible factors of a: (2, 1) ii. Possible factors of c: (7, 8), (14, 4), (28, 2) and (56, 1) iii. Work out the x term. As c is negative, select two factors of a and c that differ by b.

Factor of a with first factor of c:

 iv. As c is negative the signs of the factors are different:

 v. To check work in the opposite direction:

#### 5.   Factorise 5x2 − 20x − 60

Here a = 5, b = − 20 and c = −60

 i. Possible factors of a: (5, 1) ii. Possible factors of c: (10, 6), (12, 5), (15, 4), (20, 3), (30, 2) and (60, 1) iii. Work out the x term. As c is negative, select two factors of a and c that differ by b.

Factor of a with first factor of c:

 iv. As c is negative the signs of the factors are different:

 v. To check work in the opposite direction:

#### 6.   Factorise 3x2 − 21x + 36

Here a = 3, b = − 21 and c = 36

 i. Possible factors of a: (3, 1) ii. Possible factors of c: (6, 6), (12, 3), (9, 4), (18, 2) and (36, 1) iii. Work out the x term. As c is positive, select two factors of a and c that total to b.

Factor of a with first factor of c:

Factor of a with second factor of c:

 iv. As c is postive the signs of the factors are the same as b:(3x − 12)(x − 3)

 v. To check work in the opposite direction:

#### 7.   Factorise 3x2 − 40x + 48

Here a = 3, b = − 40 and c = 48

 i. Possible factors of a: (3, 1) ii. Possible factors of c: (6, 8), (12, 4), (16, 3), (24, 2) and (48, 1) iii. Work out the x term. As c is positive, select two factors of a and c that total to b.

Factor of a with first factor of c:

Factor of a with second factor of c:

 iv. As c is postive the signs of the factors are the same as b:(3x − 4)(x − 12)

 v. To check work in the opposite direction: back to:   