Question 1
The following quadratics can be expressed in the form (ax+b)(x+c).
Give the values of a, b and c.
1(a) 2x^2+ 14x + 24
ANSWER: Multiple Answers (Type 1)
Answer: a = 2, b = 6, c = 4
Workings:
2x^2+ 14x + 24 = (2x + 6)(x + 4)
(2x + 6)(x + 4) so a = 2, b = 6, c = 4
Marks = 2
1(b) 3x^2+ 13x + 14
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 7, c = 2
Workings:
3x^2+ 13x + 14 = (3x + 7)(x + 2)
(3x + 7)(x + 2) so a = 3, b = 7, c = 2
Marks = 2
1(c) 3x^2+ 30x + 48
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 6, c = 8
Workings:
3x^2+ 30x + 48 = (3x+6)(x+8)
(3x+6)(x+8) so a = 3, b = 6, c = 8
Marks = 2
1(d) 5x^2+ 39x + 28
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = 4, c = 7
Workings:
5x^2+ 39x + 28 = (5x+4)(x+7)
(5x+4)(x+7) so a = 5, b = 4, c = 7
Marks = 2
1(e) 5x^2+ 27x + 10
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = 2, c = 5
Workings:
5x^2+ 27x + 10 = (5x+2)(x+5)
(5x+2)(x+5) so a = 5, b = 2, c = 5
Marks = 2
Question 2
The following quadratics can be expressed in the form (ax+b)(cx+d).
Give the values of a, b, c and d, where a is greater than c.
2(a) 4x^2+ 20x + 16
ANSWER: Multiple Answers (Type 1)
Answer: a = 2, b = 8, c = 2, d = 2
Workings:
4x^2+ 20x + 16 = (2x+8)(2x+2)
(2x+8)(2x+2) so a = 2, b = 8, c = 2, d = 2.
Marks = 2
2(b) 6x^2+ 32x + 42
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 7, c = 2, d = 6
Workings:
= (3x + 7)(2x + 6)
(3x + 7)(2x + 6) so a = 3, b = 7, c = 2, d = 6
Marks = 2
2(c) 4x^2 + 18x + 8
ANSWER: Multiple Answers (Type 1)
Answer: a = 4, b = 2, c = 1, d = 4
Workings:
4x^2 + 18x + 8 = (4x + 2)(x + 4)
(4x + 2)(x + 4) so a = 4, b = 2, c = 1, d = 4
Marks = 2
2(d) 8x^2+ 46x + 30
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = 6, c = 1, d = 5
Workings:
8x^2+ 46x + 30 = (8x + 6)(x + 5)
(8x + 6)(x + 5) so a = 8, b = 6, c = 1, d = 5
Marks = 2
2(e) 9x^2+ 24x + 16
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 4, c = 3, d = 4
Workings:
9x^2+ 24x + 16 = (3x+4)(3x+4)
(3x+4)(3x+4) so a = 3, b = 4, c = 3, d = 4
Marks = 2
Question 3
The following quadratics can be expressed in the form (ax+b)(cx+d).
Give the values of a, b, c and d, where a is greater than c.
3(a) 2x^2- 18x + 16
ANSWER: Multiple Answers (Type 1)
Answer: a =2 , b = -2, c = 1, d = -8
Workings:
2x^2- 18x + 16 = (2x - 2)(x - 8)
(2x - 2)(x - 8) so a =2 , b = -2, c = 1, d = -8
Marks = 2
3(b) 7x^2 - 8x + 1
ANSWER: Multiple Answers (Type 1)
Answer: a = 7, b = -1, c = 1, d = -1
Workings:
7x^2 - 8x + 1 = (7x-1)(x-1)
(7x-1)(x-1) so a = 7, b = -1, c = 1, d = -1
Marks = 2
3(c) 6x^2- 22x + 12
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 2, c = 2, d = 6
Workings:
x^2- 22x + 12 = (3x - 2)(2x - 6)
(3x - 2)(2x - 6) so a = 3, b = 2, c = 2, d = 6
Marks = 2
3(d) 3x^2- 20x + 12
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = -2, c = 1, d = -6
Workings:
3x^2- 20x + 12 = (3x - 2)(x - 6)
(3x - 2)(x - 6) so a = 3, b = -2, c = 1, d = -6
Marks = 2
3(e) 8x^2- 26x + 6
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = -2, c = 1, d = -3
Workings:
8x^2- 26x + 6 = (8x - 2)(x-3)
(8x - 2)(x-3) so a = 8, b = -2, c = 1, d = -3
Marks = 2
Question 4
The following quadratics can be expressed in the form (ax+b)(cx+d).
Give the values of a, b c and d, where a is greater than c.
4(a) 2x^2+ 2x - 12
ANSWER: Multiple Answers (Type 1)
Answer: a = 2, b = -4, c = 1, d = 3
Workings:
2x^2+ 2x - 12 = (2x - 4)(x + 3)
(2x - 4)(x + 3) so a = 2, b = -4, c = 1, d = 3
Marks = 2
4(b) 3x^2- 20x - 32
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = 4, c = 1, d = 8
Workings:
3x^2- 20x - 32 = (3x + 4)(x - 8)
(3x + 4)(x - 8) so a = 3, b = 4, c = 1, d = 8
Marks = 2
4(c) 3x^2+ 15x - 42
ANSWER: Multiple Answers (Type 1)
Answer: a = 3, b = -6, c = 1, d = 7
Workings:
3x^2+ 15x - 42 = (3x - 6)(x+7)
(3x - 6)(x+7) so a = 3, b = -6, c = 1, d = 7
Marks = 2
4(d) 5x^2- 26x - 24
ANSWER: Multiple Answers (Type 1)
Answer: a = 5, b = 4, c = 1, d = -6
Workings:
5x^2- 26x - 24 = (5x + 4)(x - 6)
[(5x + 4)(x - 6) so a = 5, b = 4, c = 1, d = -6
Marks = 2
4(e) 7x^2- 23x - 20
ANSWER: Multiple Answers (Type 1)
Answer: a = 7, b = 5, c = 1, d = -4
Workings:
7x^2- 23x - 20 = (7x + 5)(x - 4)
(7x + 5)(x - 4) so a = 7, b = 5, c = 1, d = -4
Marks = 2
Question 5
The following quadratics can be expressed in the form (ax+b)(x+c).
Give the values of a, b and c.
5(a) 6x^2- 26x + 24
ANSWER: Multiple Answers (Type 1)
Answer: a = 6, b = -8, c = -3
Workings:
6x^2- 26x + 24 = (6x - 8)(x - 3)
(6x - 8)(x - 3) so a = 6, b = -8, c = -3
Marks = 2
5(b) 8x^2- 56x + 48
ANSWER: Multiple Answers (Type 1)
Answer: a = 8, b = -8, c = -6
Workings:
8x^2- 56x + 48 = (8x - 8)(x - 6)
(8x - 8)(x - 6) so a = 8, b = -8, c = -6
Marks = 2
5(c) 6x^2+ x - 7
ANSWER: Multiple Answers (Type 1)
Answer: a = 6, b = 7, c = -1
Workings:
6x^2+ x - 7 = (6x + 7)(x - 1)
(6x + 7)(x - 1) so a = 6, b = 7, c = -1
Marks = 2
Question 6
The following quadratics can be expressed in the form (x+a)(x+cb).
Give the values of a and b.
6(a) x^2-64
ANSWER: Simple text answer
Answer: a=8, b=-8
Workings:
x^2-64 = (x+8)(x-8)
Marks = 1
6(b) x^2 -y^2
ANSWER: Simple text answer
Answer: a=y, b=-y
Workings:
x^2 -y^2 = (x+y)(x-y)
Marks = 1