High School Maths Examples and Questions

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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 = bn × q = c
2 + 4 = 62 × 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 = bn × q = c
3 + 6 = 93 × 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 = bn × −q=−cn > q
8 − 7 = 18 × −7=−568 > 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=bn × −q=−cn > q
12 − 2=1012 × −2=−2412>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=−bn × −q=−cq > n
4 −12=−84 × −12=−4812>4

So the factors are (x + 4)(x − 12)

To verify work in the opposite direction:


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