problems with polynomials

1. Mathematics 8
Lesson 2
PROBLEMS
WITH
POLYNOMIAL
Enhancement and Consolidation Camps

2. .
Key Idea: Applying algebraic skills and understanding to solve a real-world problem
ANSWER THE FOLLOWING:
1. Expand 3(2x + 5)
2. 𝐹𝑎𝑐𝑡𝑜𝑟 24𝑎 −16 𝑎2
3. 3𝑥 2𝑥 + 7 + 6𝑥(8 − 5𝑥) + 6
4. 𝑓𝑎𝑐𝑡𝑜𝑟 𝑥2
+7x + 6
5. 𝑒𝑥𝑝𝑎𝑛𝑑 (3𝑏 − 5)2
6x + 15)
8a(3 − 2𝑎)
69x − 24𝑥2
x + 1 (x + 6)
9𝑏2
−30𝑏 + 25

3. .Lesson Component 2
(Lesson Purpose/Intention)
Time: 3 minutes
Goal:
Manipulations of
Polynomials to solve
problems

4. .
Lesson Component 3 (Lesson Language Practice)
Time: 5 minutes
Key words/terms are:
1. Expression
2. Simplest form
3. Represent
4. Perimeter
5. Area

6. Lesson Component 4B (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
1. Write an expression to represent the
south side of the garden in its simplest
form
𝟏. 𝒙 + 𝟑 + 𝟐𝒙 − 𝟒 → 𝟑𝒙 − 𝟏

7. Lesson Component 4B (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
2. Write an expression to represent the
perimeter of the garden in its simplest
form.
𝟐. 𝟐𝒙 + 𝟒 + 𝒙 + 𝟐 + 𝒙 + 𝟑 + 𝟐𝒙 − 𝟒 + 𝒙 + 𝟏
+ 𝟐𝒙 + 𝟓 + 𝒙 + 𝟑 + 𝟐𝒙 − 𝟒 = 𝟏𝟐𝒙 + 𝟏𝟎

8. Lesson Component 4B (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
3. Why would this expression be useful
for Joe?
3. If he wanted to enlarge the size of the
garden, he could still determine the
measurements by changing the value of x

9. Lesson Component 4B (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
4. Write a polynomial expression for
the area of the carnations plot.
4. (𝒙 + 𝟐)(𝒙 + 𝟑) = 𝒙𝟐
+ 𝟓𝒙 + 𝟔

10. Lesson Component 4C (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
1. Write expression to show the
perimeter of the violets in its simplest
form.
1. 𝒙 + 𝟑 + 𝟐𝒙 + 𝟒 + 𝒙 + 𝟑 + 𝟐𝒙 + 𝟒 = 𝟔𝒙 + 𝟏𝟒
= 𝟐(𝟑𝒙 + 𝟕)

11. Lesson Component 4C (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
2. Write expression to show the area of
the whole garden in its simplest form.
2. 𝟐𝒙 + 𝟒 + 𝒙 + 𝟐 ∗ (𝒙 + 𝟑 + 𝟐𝒙 − 𝟒)
= 𝟗𝒙𝟐
+ 𝟑𝒙 − 𝟔

12. Lesson Component 4C (Lesson activity)
.
Time: 5 minutes
Let’s answer this!
3. Write a different expression for the
area of the whole garden.
2. 𝟐𝒙 + 𝟓 + 𝒙 + 𝟏 ∗ (𝒙 + 𝟑 + 𝟐𝒙 − 𝟒)
= 𝟗𝒙𝟐
+ 𝟑𝒙 − 𝟔

13. Lesson Component 5 (Lesson Conclusion – Reflection/Metacognition on
.Student Goals)
Time: 5 minutes
o What do you think were the key mathematical concepts addressed in this
lesson?
o Would you rate your level of understanding of the material covered in
this lesson as high, moderate, or low?
o Has the lesson helped you to gain further insight into aspects of the
material covered that represent strengths or represent weaknesses?
o What would you describe as the main barriers, if any, to your ongoing
progress and achievement in relation to the topic area addressed in this
lesson?
o What do you think would best assist your ongoing progress and
achievement in relation to the topic area?