# 8. Factor : 3y(x – 3) –2(x – 3)

1. Which is greater than 4 ?
(a) 5
(b) –5
(c) –$$\frac{1}{2}$$
(d) –25

description :
5 greater than 4

2. Which is the smallest ?
(a) 1
(b) –$$\frac{1}{2}$$
(c) 0
(d) 3

description :
The smallest number is –1

3. Combine terms: 12a + 26b – 4b – 16a
(a) 4a + 22b
(b) –28a + 30b
(c) 4a + 22b
(d) 28a + 30b

description :
12a + 26b – 4b – 16a
= 12a – 16a + 26b – 4b
= –4a + 22b

4. Simplify: (4 – 5) – (13 – 18 + 2)
(a) –1
(b) –2
(c) 1
(d) 2

description :
(4 – 5) – (13–18+2)
= –1 – (–5+2)
= –1 – (–3)
= –1 + 3
= 2

5. What is | –26 | ?
(a) –26
(b) 26
(c) 0
(d) 1

description :
| –26 |
= 26

6. Multiply: (x–4)(x+5)
(a) $$x^{2}$$ + 5x – 20
(b) $$x^{2}$$ – 4x – 20
(c) $$x^{2}$$ – x – 20
(d) $$x^{2}$$ + x  20

description :
(x – 4)(x + 5)
= $$x^{2}$$ + 5x – 4x – 20
= $$x^{2}$$ + x – 20

7. Factor : $$5x^{2}$$ – 15x – 20
(a) 5(x4)(x+1)
(b) –2(x–4)(x+5)
(c) –5(x+4)(x–1)
(d) 5(x+4)(x+1)

description :
$$5x^{2}$$ – 15x – 20
= 5($$x^{2}$$ – 3x – 4)
= 5(x–4)(x+1)

8. Factor : 3y(x – 3) –2(x – 3)
(a) (x–3)(x–3)
(b) (x–3)2
(c) (x–3)(3y–2)
(d) 3y(x – 3)

description :
3y(x – 3) –2(x – 3)
= 3xy – 9y – 2x + 6
= (x – 3)(3y – 2)

9. Solve for x: 2x – y = $$(\frac{3}{4})$$x + 6
(a) $$\frac{(y + 6)}{5}$$
(b) $$\frac{4(y + 6)}{5}$$
(c) (y + 6)
(d) $$\frac{4(y - 6)}{5}$$

description :
2x – y = $$(\frac{3}{4})$$x + 6
2x – $$(\frac{3}{4})$$x = y + 6
$$\frac{8x}{4}$$ – $$\frac{3x}{4}$$ = y + 6
$$\frac{5x}{4}$$ = y + 6
5x = 4(y + 6)
x = $$\frac{4(y+6)}{5}$$

10. Simplify : (4$$x^{2}$$–2x) – (–5$$x^{2}$$–8x)

description :
(4$$x^{2}$$–2x) – (–5$$x^{2}$$–8x)
= 4$$x^{2}$$ – 2x + 5$$x^{2}$$ – 8x
= 4$$x^{2}$$ + 5$$x^{2}$$ – 2x + 8x
= 9$$x^{2}$$ + 6x
= 3x(3x+2)

11. Find the value of 3 + 2 • (8 – 3)
(a) 25
(b) 13
(c) 17
(d) 24
(e) 15

description :
3 + 2 • (8 – 3)
= 3 + 2 (5)
= 3 + 2 × 5
= 3 + 10
= 13

12. Rice weighing 3$$\frac{3}{4}$$ pounds was divided equally and placed in 4 containers. How many ounces of rice were in each?

description :
3$$\frac{3}{4}$$ ÷ 4 pounds
= $$\frac{15}{4}$$ ÷ 4 pounds
= $$\frac{15}{4}$$ × $$\frac{1}{4}$$ pounds
= $$\frac{15}{16}$$ pounds (1 container)
1 pound = 16 ounces
= $$\frac{15}{16}$$ × 16 ounces
= 15 ounces

13. Factor: 16$$w^{3}$$ – $$u^{4}w^{3}$$

description :
16$$w^{3}$$ – $$u^{4}w^{3}$$
= $$w^{3}$$(16 – $$u^{4}$$)
= $$w^{3}$$(4 + $$u^{2}$$)(4 – $$u^{2}$$)
= $$w^{3}$$(4 + $$u^{2}$$)(2 + u)(2 – u)

14. Factor: 3$$x^{4}y^{3}$$ – 48$$y^{3}$$

description :
3$$x^{4}y^{3}$$ – 48$$y^{3}$$
= 3$$y^{3}$$($$x^{4}$$ – 16)
= 3$$y^{3}$$($$x^{2}$$ + 4)($$x^{2}$$ – 4)
= 3$$y^{3}$$($$x^{2}$$ + 4)(x + 2)(x–2)

15. What is the radius of a circle that has a circumference of 3.14 meters ?

description :
circle circumference formula = 2πr
circumference = 3.14 meters
2πr = Circumference of a circle
2πr = 3.14
2 × 3.14 x r = 3.14
6.28r = 3.14
r = $$\frac{3.14}{6.28}$$
r = 0.5