Question 1
The following quadratics can be expressed in the form (x+a)(x+b).
Give the values of a and b where a is greater (more positive) than b.
1(a) x^2+ 14x + 48
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = 6
Workings:
x^2+ 14x + 48 = (x + 8)(x + 6)
(x + 8)(x + 6) so a = 8, b = 6
Marks = 2
1(b) x^2+ 13x + 42
ANSWER: Multiple Answers (Type 1)
Answer: a = 7, b = 6
Workings:
x^2+ 13x + 42 = (x + 7)(x + 6)
(x + 7)(x + 6) so a = 7, b = 6
Marks = 2
1(c) x^2+ 10x + 16
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = 2
Workings:
x^2+ 10x + 16 = (x + 2)(x + 8)
(x + 2)(x + 8) so a = 8, b = 2
Marks = 2
1(d) x^2+ 8x + 7
ANSWER: Multiple Answers (Type 1)
Answer: a = 7, b = 1
Workings:
x^2+ 8x + 7 = (x +7)(x + 1)
(x + 7)(x + 1) so a = 7, b = 1
Marks = 2
1(e) x^2+ 12x + 32
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = 4
Workings:
x^2+ 12x + 32 = (x +8)(x + 4)
(x + 8)(x +4) so a = 8, b = 4
Marks = 2
Question 2
The following quadratics can be expressed in the form (x+a)(x+b).
Give the values of a and b where a is greater (more positive) than b.
2(a) x^2- 10x + 24
ANSWER: Multiple Answers (Type 1)
Answer: a = -4, b = -6
Workings
x^2- 10x + 24 = (x - 4)(x - 6)
(x - 4)(x - 6) so a = -4, b = -6
Marks = 2
2(b) x^2- 11x + 28
ANSWER: Multiple Answers (Type 1)
Answer: a = -4, b = -7
Workings:
x^2- 11x + 28 = (x-4)(x-7)
(x-4)(x-7) so a = -4, b = -7
Marks = 2
2(c) x^2- 11x + 30
ANSWER: Multiple Answers (Type 1)
Answer: a = -5, b = -6
Workings:
x^2- 11x + 30 = (x-5)(x-6)
(x-5)(x-6) so a = -5, b = -6
Marks = 2
2(d) x^2- 8x + 15
ANSWER: Multiple Answers (Type 1)
Answer: a = -3, b = -5
Workings:
x^2- 8x + 15 = (x-3)(x-5)
(x-3)(x-5) so a = -3, b = -5
Marks = 2
2(e) x^2- 4x + 4
ANSWER: Multiple Answers (Type 1)
Answer: a = -2, b = 2
Workings:
x^2- 4x + 4 = (x-2)(x-2)
(x-2)(x-2) so a = -2, b = -2
Marks = 2
Question 3
The following quadratics can be expressed in the form (x+a)(x+b)
Give the values of a and b where a is greater (more positive) than b.
3(a) x^2+ x - 30
ANSWER: Multiple Answers (Type 1)
Answer: a = 6, b = -5
Workings:
x^2+ x - 30 = (x+6)(x-5)
(x+6)(x-5) so a = 6, b = -5
Marks = 2
3(b) x^2+ 2x - 35
ANSWER: Multiple Answers (Type 1)
Answer: a = 7, b = -5
Workings:
x^2+ 2x - 35 = (x+7)(x-5)
(x+7)(x-5) so a = 7, b = -5
Marks = 2
3(c) x^2+ 4x - 5
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = -1
Workings:
x^2+ 4x - 5 = (x+5)(x-1)
(x+5)(x-1) so a = 5, b = -1
Marks = 2
3(d) x^2- x - 2
ANSWER: Multiple Answers (Type 1)
Answer: a = 1, b = -2
Workings:
x^2- x - 2 = (x+1)(x-2)
(x+1)(x-2) so a = 1, b = -2
Marks = 2
3(e) x^2- 4x - 5
ANSWER: Multiple Answers (Type 1)
Answer: a = 1, b = -5
Workings:
x^2- 4x - 5 = (x+1)(x-5)
(x+1)(x-5) so a = 1, b = -5
Marks = 2
Question 4
The following quadratics can be expressed in the form (x+a)(x+b)
Give the values of a and b where a is greater (more positive) than b.
4(a) x^2- 3x - 40
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = -8
Workings:
x^2- 3x - 40 = (x+5)(x-8)
(x+5)(x-8) so a = 5, b = -8
Marks = 2
4(b) x^2+ 5x + 4
ANSWER: Multiple Answers (Type 1)
Answer: a = 4, b = 1
Workings:
x^2+ 5x + 4 = (x+4)(x+1)
(x+4)(x+1) so a = 4, b = 1
Marks = 2
4(c) x^2+ 3x - 18
ANSWER: Multiple Answers (Type 1)
Answer: a = 6, b = -3
Workings:
x^2+ 3x - 18 = (x+6)(x-3)
(x+6)(x-3) so a = 6, b = -3
Marks = 2
4(d) x^2+ x - 2
ANSWER: Multiple Answers (Type 1)
Answer: a = 2, b = -1
Workings:
x^2+ x - 2 = (x+2)(x-1)
(x+2)(x-1) so a = 2, b = -1
Marks = 2
4(e) x^2- 6x + 5
ANSWER: Multiple Answers (Type 1)
Answer: a = -1, b = -5
Workings:
x^2- 6x + 5 = (x-1)(x-5)
(x-1)(x-5) so a = -1, b = -5
Marks = 2