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) x2+14x+48
ANSWER: Multiple Answers (Type 1)
Answer: a=8, b=6
Workings:
x2+14x+48=(x+8)(x+6)
(x+8)(x+6) so a=8, b=6
Marks = 2
1(b) x2+13x+42
ANSWER: Multiple Answers (Type 1)
Answer: a=7, b=6
Workings:
x2+13x+42=(x+7)(x+6)
(x+7)(x+6) so a=7, b=6
Marks = 2
1(c) x2+10x+16
ANSWER: Multiple Answers (Type 1)
Answer: a=8, b=2
Workings:
x2+10x+16=(x+2)(x+8)
(x+2)(x+8) so a=8, b=2
Marks = 2
1(d) x2+8x+7
ANSWER: Multiple Answers (Type 1)
Answer: a=7, b=1
Workings:
x2+8x+7=(x+7)(x+1)
(x+7)(x+1) so a=7, b=1
Marks = 2
1(e) x2+12x+32
ANSWER: Multiple Answers (Type 1)
Answer: a=8, b=4
Workings:
x2+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) x2−10x+24
ANSWER: Multiple Answers (Type 1)
Answer: a=−4, b=−6
Workings
x2−10x+24=(x−4)(x−6)
(x−4)(x−6) so a=−4, b=−6
Marks = 2
2(b) x2−11x+28
ANSWER: Multiple Answers (Type 1)
Answer: a=−4, b=−7
Workings:
x2−11x+28=(x−4)(x−7)
(x−4)(x−7) so a=−4, b=−7
Marks = 2
2(c) x2−11x+30
ANSWER: Multiple Answers (Type 1)
Answer: a=−5, b=−6
Workings:
x2−11x+30=(x−5)(x−6)
(x−5)(x−6) so a=−5, b=−6
Marks = 2
2(d) x2−8x+15
ANSWER: Multiple Answers (Type 1)
Answer: a=−3, b=−5
Workings:
x2−8x+15=(x−3)(x−5)
(x−3)(x−5) so a=−3, b=−5
Marks = 2
2(e) x2−4x+4
ANSWER: Multiple Answers (Type 1)
Answer: a=−2, b=2
Workings:
x2−4x+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) x2+x−30
ANSWER: Multiple Answers (Type 1)
Answer: a=6, b=−5
Workings:
x2+x−30=(x+6)(x−5)
(x+6)(x−5) so a=6, b=−5
Marks = 2
3(b) x2+2x−35
ANSWER: Multiple Answers (Type 1)
Answer: a=7, b=−5
Workings:
x2+2x−35=(x+7)(x−5)
(x+7)(x−5) so a=7, b=−5
Marks = 2
3(c) x2+4x−5
ANSWER: Multiple Answers (Type 1)
Answer: a=5, b=−1
Workings:
x2+4x−5=(x+5)(x−1)
(x+5)(x−1) so a=5, b=−1
Marks = 2
3(d) x2−x−2
ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=−2
Workings:
x2−x−2=(x+1)(x−2)
(x+1)(x−2) so a=1, b=−2
Marks = 2
3(e) x2−4x−5
ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=−5
Workings:
x2−4x−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) x2−3x−40
ANSWER: Multiple Answers (Type 1)
Answer: a=5, b=−8
Workings:
x2−3x−40=(x+5)(x−8)
(x+5)(x−8) so a=5, b=−8
Marks = 2
4(b) x2+5x+4
ANSWER: Multiple Answers (Type 1)
Answer: a=4, b=1
Workings:
x2+5x+4=(x+4)(x+1)
(x+4)(x+1) so a=4, b=1
Marks = 2
4(c) x2+3x−18
ANSWER: Multiple Answers (Type 1)
Answer: a=6, b=−3
Workings:
x2+3x−18=(x+6)(x−3)
(x+6)(x−3) so a=6, b=−3
Marks = 2
4(d) x2+x−2
ANSWER: Multiple Answers (Type 1)
Answer: a=2, b=−1
Workings:
x2+x−2=(x+2)(x−1)
(x+2)(x−1) so a=2, b=−1
Marks = 2
4(e) x2−6x+5
ANSWER: Multiple Answers (Type 1)
Answer: a=−1, b=−5
Workings:
x2−6x+5=(x−1)(x−5)
(x−1)(x−5) so a=−1, b=−5
Marks = 2
