mathematics 10 quarter two teaching material powerpoint presentation

1. ILLUSTRATING
POLYNOMIAL FUNCTIONS
GRADE 10 – MATHEMATICS
SIR KYLE

2. LESSON OBJECTIVES
Identify polynomial functions. Illustrate polynomial
functions.
Value accumulated
knowledge as means of new
understanding.

4. 1. 14𝑥
2. 5𝑥2
− 4 2𝑥 + 𝑥
3. 𝛱
4. 𝑥
3
4 + 3𝑥
1
4 + 7
5. −4𝑥−100
+ 4𝑥100
FACT OR BLUFF
Write FACT if the expression
being shown is a polynomial,
otherwise write BLUFF.

5. USING THE POLYNOMIAL
FUNCTION
𝑃 𝑥 = 6𝑥3
+ 4𝑥2
+ 6
1. How many terms are there?
2. What is the degree of the polynomial?
3. What is the leading coefficient?
4. How about the constant term?

6. USING THE POLYNOMIAL
FUNCTION
࢟ = ૞࢞૛ + ૛࢞૜ − ࢞૝ + ૜
1. How many terms are there?
2. What is the degree of the polynomial?
3. What is the leading coefficient?
4. How about the constant term?

7. DEFINITION OF TERMS
A polynomial function is a function in the form
𝑷(࢞) = 𝒂𝒏࢞𝒏 + 𝒂𝒏−𝟏࢞𝒏−𝟏 + 𝒂𝒏−૛࢞𝒏−૛ + ⋯+ 𝒂𝟏࢞𝟏 + 𝒂𝟎,
where 𝑛 is a nonnegative integer, n as a positive integer implies that:
a. n is not negative
b. n is not zero
c. n is not a fraction
d. n is not a radical, and
e. n is not imaginary
𝑎0, 𝑎1, … , 𝑎𝑛are real numbers called coefficients, 𝑎𝑛𝑥𝑛 is the leading
term, 𝑎𝑛 is the leading coefficient, and 𝑎0 is the constant term.

8. NOTE
Polynomials may also be written in
factored form and as a product of
irreducible factors, that is a factor
can no longer be factored using
coefficients that are real numbers.
The function 𝑦 = 𝑥4 + 2𝑥3 − 13𝑥2 −
10𝑥 in factored form is 𝑦 = (𝑥 − 5)(
𝑥 + 1)(𝑥 + 2).

9. FIX AND MOVE THEM,
THEN FILL ME UP

10. DIRECTION: Consider the given polynomial functions
and fill in the table below.
Polynomial Function Standard
Form
Degree Leading
Coefficient
Constant
𝟏. 𝑓 𝑥 = 2 − 11𝑥 + 2𝑥2
𝟐. 𝑓 𝑥 =
2𝑥3
3
+
5
3
+ 15𝑥
𝟑. 𝑓 𝑥 = 𝑥(𝑥 − 3)
𝟒. 𝑓 𝑥 = 𝑥(𝑥2 − 5)
𝟓. 𝑦 = 3𝑥3 + 2𝑥 − 𝑥4

11. ANALYSIS
When are functions
polynomials?
How can we
determine the
degree of a
polynomial function?
In a polynomial
function, which is
the leading
coefficient? Constant
term?

12. TELL WHETHER THE FOLLOWING IS A POLYNOMIAL
FUNCTION OR NOT. GIVE THE DEGREE AND THE
NUMBER OF TERMS FOR POLYNOMIAL FUNCTIONS.
1. 𝑦 = 3𝑥2 − 2𝑥 + 4
2. 𝑦 = 5𝑥+3
3. 𝑦 =
𝑥 + 4
3
4. 𝑦 = 𝑥 − 4 4𝑥 + 1
5. 𝑦 = 6𝑥2 + 1

13. USE ALL THE NUMBERS
IN THE BOX ONCE AS
COEFFICIENTS OR
EXPONENTS TO FORM
AS MAY POLYNOMIAL
FUNCTIONS OF X AS
YOU CAN. WRITE YOUR
POLYNOMIAL
FUNCTION IN
STANDARD FORM

14. GENERALIZATION
A polynomial function is a function in the form
𝑷(࢞) = 𝒂𝒏࢞𝒏 + 𝒂𝒏−𝟏࢞𝒏−𝟏 + 𝒂𝒏−૛࢞𝒏−૛ + ⋯+ 𝒂𝟏࢞𝟏 + 𝒂𝟎,
where 𝑛 is a nonnegative integer, n as a positive integer implies that:
a. n is not negative
b. n is not zero
c. n is not a fraction
d. n is not a radical, and
e. n is not imaginary
𝑎0, 𝑎1, … , 𝑎𝑛are real numbers called coefficients, 𝑎𝑛𝑥𝑛 is the leading
term, 𝑎𝑛 is the leading coefficient, and 𝑎0 is the constant term.

15. END OF PRESENTATION