Polynomials.pdf Long & Synthetic Division Remainder and Factor Theorem

Long & Synthetic Division
Remainder and Factor Theorem

1. MathematicsMathematics
10A10A
Kassandra Venzuelo - Alayon
Ramon Teves Pastor Memorial-Dumaguete Science High School

2. PolynomialsPolynomials
Long & Synthetic Division
Remainder and Factor Theorem

3. LessonLesson
ObjectivesObjectives
define and identify
polynomials(degree,
leading term& coefficient,
etc.)
perform long and synthetic
division;
prove Factor and
Remainder Theorem

4. WHAT ARE
POLYNOMIALS?

5. WHAT IS A POLYNOMIAL?
A polynomial is a mathematical expression made up of variables
(also called indeterminates), coefficients, and exponents,
combined using only addition, subtraction, and multiplication. The
exponents of the variables must be whole numbers (non-negative
integers), and the coefficients can be real (or complex) numbers.

7. Is the expression a
polynomial? Yes or No.
Why?

9. WHEN IT’S NOT A POLYNOMIAL

10. Examples

11. DEGREE OF
POLYNOMIAL
EXPRESSIONS

13. After degree 10, expressions are usually just called “11th-degree polynomial,” “12th-
degree polynomial,” and so on.

14. LEADING
TERM &
COEFFICIENT

15. Leading term is the
term with the highest
degree and the leading
coefficient is that term’s
coefficient.

16. ACTIVITY 1

19. LONG
DIVISION

20. 755
15
Quotient
Divisor
Dividend
VOCAB:

25. SYNTHETIC
DIVISION

28. PRESENTATION
Group Borcelle

32. ACTIVITY 2ACTIVITY 2

35. PERFORMANCE
TASK
PERFORMANCE
TASK

36. GEOMETRIC SEQUENCE
AND SERIES

37. “Design a Savings Plan Using a Geometric Sequence”
Objective:
You will create a real-life financial savings plan based on a geometric sequence and
analyze how your money grows over time. This task will demonstrate your understanding
of geometric sequences, series, and their applications.

38. Scenario:
Imagine you are starting a savings plan. You
decide to deposit an amount of money every
month into a bank account, and each month, you
increase your deposit by a fixed common ratio.

39. Your Task:
1.Choose a starting amount (first term) for your monthly deposit.
2.Choose a common ratio (how much the amount will multiply by each month).
3.Create a geometric sequence representing your monthly deposits for at least 6 months.
4.Find the total amount saved after 6 months using the formula for the sum of a
geometric series.
5.Create a graph showing the growth of your deposits over time.
6.Write a 1-paragraph reflection explaining:
Why you chose your values.
What the sequence and series represent.
What insights you gained about geometric growth.

40. Presentation Format:
One-page report (typed or neatly handwritten)
Include:
The sequence
Calculations
Graph (hand-drawn or digital)
Reflection paragraph

41. RUBRICSRUBRICS

42. Thank you!Thank you!
StaL safe!StaL safe!