Page 19 - Algebra 1

Explanation
1. x2 –6√3x+15
Split the middle term
=x2 –5√3x–√3x+15
= x (x –5√3) – √3 (x – 5√3) = (x –√3) (x –5√3)
2. x4+64
Add and subtract 16x2
=x4 +64+16x2–16x2
=(x2 + 8)2 – (4x)2
Usetheidentitya2 –b2 =(a+b)(a–b) =(x2 +8–4x)(x2 +8+4x)
3. Let the salary of one day be x
𝑥
2
16x + 4x – 30 = 300
20x = 330
x = $16.5
Salary paid to an electrician for 30 days = 16.5 × 30 = $495
4.
16x + 8 ×
- 6 × 5 = 300
Let the number of questions in the exam be x
No. of questions attempted by Babis = 0.80x
No. of correct questions = 0.60 × 0.80x = 0.48x
No. of incorrect questions = 0.40 × 0.80x = 0.32x
0.48x × 4 + 0.32x × (–1) = 320
1.92x
1.6x = 320 x = 200
5.
= 2𝑥+7 2𝑥− 1
6.
4𝑥2 –49
– 0.32x = 320
4𝑥2− 16𝑥 + 7
=
(2𝑥)2 –72
4𝑥2− 14𝑥−2𝑥 + 7
=
(2𝑥 –7)(2𝑥+7)
2𝑥(2𝑥− 7)−1(2𝑥− 7)
=
(2𝑥 –7)(2𝑥+7)
(2𝑥− 7)(2𝑥− 1)
Let the numerator be x
The denominator is 12 – x
Page 18 of 54
ALGEBRA