Answer:
Task 1
1. C
2. A
3. D
4. B
5. E
Task 2
1. [tex](x-3)(x+6)[/tex]
2. [tex]3(x-4)(x+1)[/tex]
3. [tex]3(6x-5)(x+1)[/tex]
4. [tex](5x+2)(x+6)[/tex]
5. [tex]3(x^{2} +8)[/tex]
Task 3
1. The Number is 9
Translating Phrases to Algebraic Expressions
Let x be the number.
"square of a number" = x²
"nine times that number" = 9x
Algebraic Equation
"The square of a number equals nine times that number."
x² = 9x
Solution:
x² = 9x
x²/x = 9x/x
x = 9
Final Answer:
The number is 9.
Checking:
x² = 9x
(9)² = 9(9)
81 = 81 ✔
2. The Number is 5
Equation:
Let "x" be the number.
"four times the square of a number" = 4x²
"20 times that number" = 20x
"four times the square of a number equals 20 times that number"
4x² = 20x
Solution:
4x² = 20x
4x²/4x = 20x/4x
x = 5
Final Answer:
The number is 5.
Checking:
To check, substitute the number.
4x² = 20x
4(5²) = 20(5)
4(25) = 100
100 = 100 ✔
3. The Number is 4 and 10
Let x be the number
Square of the sum of a number and 3
[tex](x+3)^{2}[/tex]
Twice the square of the sum of a number and 3
[tex]2(x+3)^{2}[/tex]
Twice the square of the sum of a number and 3 is 98
[tex]2(x+3)^{2}=98[/tex]
Dividing both sides by two
[tex](x+3)^{2}=49[/tex]
Applying square root on both sides
[tex]=\sqrt{(x+3)^2}[/tex][tex]=\sqrt{49}[/tex]
x+3 = ±7
The equation therefore is
x+3 = 7 ; x+3 = - 7
Isolating x;
x+3 = 7
x = 7-3
x = 4
=======
x+3 = - 7
x = - 7 -3
x = -10
Therefore the answer is 4 and -10
Checking:
[tex]2(x+3)^2=98[/tex]
Substituting the value:
x = 4
2(4+3)² = 98
2(49) = 98
98 = 98✔
When x = -10
2(-10+3)² = 98
2(49)= 98
98 =98✔
Task 4
1. [tex](x+5)(x-5)[/tex]
2. [tex](2x+1)(x-8)[/tex]
3. [tex]3 (x^{2} +35)[/tex]
4. [tex](x-3)(x^{2} +3x+9)[/tex]
5. [tex]5x (x-2)(x+1)[/tex]
