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:

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