first quarter topic for grade 10

1. Illustrating
Polynomial Equations

2. What is a Polynomial Equation?
A polynomial equation/function is a
function of the form,
= 0
where is a nonnegative integer, are real
numbers called coefficients,
is the leading term,
is the leading coefficient, and
is the constant term.

4. From the definition, the following are implied:
i. No negative exponent.
ii. No fraction or decimal exponent.
iii. No variables in the denominator.
iv. No variables under the radical sign.

5. Examples of Polynomial Equations
1.
Standard Form: 3 𝑥4
−2 𝑥3
+7 𝑥2
+𝑥 −15=0
Leading Term:
3 𝑥 4
Leading Coefficient:
3
Constant Term:
− 15
Degree:
4

6. 2.
Standard Form:
−
2
3
𝑥
5
+
4
5
𝑥
3
−
1
2
𝑥 +27=0
Leading Term:
−
2
3
𝑥
5
Leading Coefficient:
−
2
3
Constant Term:
27
Degree:
5

7. 3.
Standard Form:
𝑥3
+ 2 𝑥2
− 15 𝑥=0
Leading Term:
𝑥 3
Leading Coefficient:
1
Constant Term:
0
Degree:
3

8. Examples of Non-Polynomial Equations
1.
2.
3.
4.

9. Complete the table. Write the equations in standard form, then
determine the degree, the leading coefficient, and the constant
term.
Polynomial
Function
Standard
Form
Degre
e
Leading
Coefficien
t
Constan
t
Term

11. FIND THE ROOTS OF THE FOLLOWING
EQUATION.
1. (3x + 2)(

12. SOLVE THE GIVEN PROBLEM
Recycling is a way we can all do our part to help
keep the earth clean. Mr. Flores a grade 5 science
teacher wants to recycle a used cardboard into a
box. The length of the box is 6 inches longer
than the height and the width is 3 inches less
than the height. If the volume of the box is 810
inches, how will you represent the dimensions of
the box in polynomial equation?

13. A polynomial equation/function is a function of the
form,
where is a nonnegative integer, are real
numbers called coefficients, is the leading term, is the
leading coefficient, and is the constant term.
i. No negative exponent.
ii.No fraction or decimal exponent.
iii.No variables in the denominator.
iv.No variables under the radical sign.

14. Answer the following. Choose the letter of the correct answer.
1. What term refers to the highest exponent
in a polynomial?
A. coefficient
B. degree
C. exponent
D. leading term

15. 2. What is the leading term of the polynomial
equation: 2x3
+ x4
- 6x +12 = 0?
A. 2x3
B. x4
C. - 6x
D. 12

16. 3. What is the constant term of the
polynomial equation: 5x3
+ x2
- 10x - 7 = 0?
A. 5x3
B. x2
C. - 10x
D. -7

17. 4. Which of the following is the standard
form of P(x)=x3
+ 3x4
- 5x + 6?
A. P(x)= x3
+ 3x4
- 5x + 6
B. P(x)= x3
- 5x + 3x4
+ 6
C. P(x)= 3x4
+ x3
- 5x + 6
D. P(x)= 3x4
- x3
- 5x + 6

18. 5. Which of the following is/are
example(s) of a polynomial equation.
i.
ii. x3
+ - x + 5 = 0
iii. 5 – x – 5x2
+ x3
= 0
A. i only B. i and ii only

19. 6. What are the roots of
(2x + 1) (x + 1)(x – 1)=0?
A. -1/2, -1, 1
B. 2, 1, -1
C. ½, 1, -1
D. -2, -1, 1

20. 7.Which of the following are the zeros of
the polynomial equation + - -14x + 24=0.
A. 1, 2, 3, 4
B. -4, -2, 1, 3
C. -4, -3, 1, 2
D. -4, -3, 1, 2

21. 8. Which of among the polynomial
equations has roots -2, 3, and -5?
A.x3
- 4x2
+ 11x - 30 = 0
B.x3
+ 3x2
- 12x + 30 = 0
C.x3
+ 3x2
- 10x + 30 = 0
D.x3
+ 4x2
- 11x - 30 = 0

22. 9. Which of the following is NOT a
root of (x - 2)(x -1)(x – 1)(2x - 1) = 0?
i. 0 ii. -2 iii. 1 iv. ½
A. i only C. i and ii only
B. ii only D. iii and iv

23. 10. How many zeros does the polynomial
function
3x4
+4x-8 = 0 have?
A. 1
B. 2
C. 3
D. 4

24. Write the following polynomials in standard
form then, determine the leading term,
leading coefficient, constant term and the
degree of the polynomials.

25. Thanks and God
bless!!!
ARZEL S. MENDOZA
Teacher II
Mathematics Department