### Answers − Factorising quadratics of the form ax^{2} + bx + c, where a is not equal to 1

#### 1. Factorise 2x^{2} + 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 3x^{2} + 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 4x^{2} + 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 2x^{2} + 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 5x^{2} − 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 3x^{2} − 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 3x^{2} − 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: |

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