The document outlines a mathematics lesson plan focused on polynomials, including their definition, characteristics, types, and operations such as addition, subtraction, and long division. It presents step-by-step methods for dividing polynomials and introduces synthetic division as an alternative approach. Additionally, it includes guided questions and practical applications to help students relate polynomial concepts to real-life situations.

1. POLYNOMIALS
Mathematics 10 | Quarter 1

2. PRAYER

4. LESSON OBJECTIVES
Illustrate a
polynomial.
Perform long
division on
polynomials.
Appreciate the
use of the
concept learned
in real-life
situation.

5. RECALL
Characteristics of Polynomial
Definition of Polynomial
Types of Polynomial
Degree of Polynomial
Addition and Subtraction of
Polynomial

6. CLASSIFYING POLYNOMIALS
Direction: Complete the table.

8. ADDING AND SUBTRACTING
POLYNOMIALS
Direction: Add and/or subtract the given
polynomials completely.

11. Guide Question:
a. Will you able to know the steps in
division?
b. What will happen when you skip the
multiplication part?
c. Can you relate it in a real-life situation?
Cite examples.

12. DIVIDING POLYNOMIALS
Long Method

13. ILLUSTRATIVE EXAMPLE
Let us divide;

14. Step 1 :
Set up the long division.

15. Step 2 :
Divide the first term of the dividend
by the first term of the divisor to
get the first term of the quotient.

16. Step 3 :
Take the term found in step
2 and multiply it to the
divisor.

17. Step 4 :
Subtract this from the
line above.

18. Step 5 :
Repeat until done.

19. Step 6 :
Write out the answer.

20. APPLY YOUR SKILLS
Direction: Find the quotient and the
remainder by using the long division.
Write your complete solution.

21. ( 𝑥
2
+3 𝑥+10 ) ÷(𝑥 +2)
(10 𝑥3
+5 𝑥2
+75 𝑥 − 40 )÷(2 𝑥+1)
Quotient: __________ Remainder :
___________
Quotient: __________ Remainder :
___________

22. SOLVE, then DECIDE
Direction: Read the questions carefully
and choose the letter of the best answer.

23. TESTING YOUR KNOWLEDGE
Direction: Read and analyze the given
situation and apply the learnings gained in
dividing polynomials.

25. DIVIDING POLYNOMIALS
Synthetic Division

26. Step 1 :
Arrange the coefficients of P(x) in
descending powers of x, placing 0’s for
the missing terms. The leading
coefficient of P(x) becomes the first
entry of the third row.

27. Step 2 :
Place the value of r in the upper
left corner.

28. Step 3 :
The first number in the second row is the
product of r and the number in the third
row of the preceding column. The second
number in the third row is the sum of the
two numbers above it.

29. Step 4 :
Repeat the procedure described
in Step 3 until the last number
in the third row is obtained.

30. Step 5 :
Write the quotient Q(x). Note that the
degree of the Q(x) is one less than the
degree of the P(x). The entries in the third
row give the coefficients of Q(x) and the
remainder R.

31. “ Believing in yourself …
is always the ‘x’ factor in the equation
of achieving greatness”
--- Timothy Pina