powerpoint presentation

2. Let’s Prepare
Determine whether the underlined word or group of
words represent addition, subtraction, multiplication, or
division.
1. Eight added to a certain number = 8 + b
2. The quotient of a number and eleven =
𝑥
11
3. A number decreased by 5
4. Nine greater than a certain number
5. The product of four and x

3. Let’s Learn
The following examples show how verbal phrases
are translated to mathematical symbols.
Operation Verbal Phrase Mathematical
Symbols
Addition
the sum of 3 and 4 3 + 4
m increased by 5 m + 5
k added to 7 7 + k

4. Operation Verbal Phrase Mathematical
Symbols
Subtraction the difference between
x and y
x - y
subtract x from eleven
11 - x
m decreased by 8
m - 8
n reduced by 6 n - 6
14 less f 14 - f

5. Operation Verbal Phrase Mathematical
Symbols
Multiplication
the product of x and y xy
13 times y 13y
twice m 2m

6. Operation Verbal Phrase Mathematical
Symbols
Division
the ratio of m and n 𝑚
𝑛
The quotient of r and 5 𝑟
5
15 divided by x 15
𝑥

7. Understanding Algebraic Expression
An algebraic expression is a mathematical expression consist of
a variable, constant, or a combination of a variable and constant
related by at least one operation.
Variable – is a letter that can stand as a various number.
Constant – is a number, or symbol (3.14) that has a fixed value.
The following are the examples of an algebraic expression:
x -3 xy 5x -4bx2
x + y 2y x3 – 2 3b2 2𝑚
𝑛

8. Study the following:
Algebraic Expression Variable/s Constant/s
1. x = 1x x 1
2. xy x, y 1
3. 4x - 2 x 4, -2
4. 3y2 y 3
5. 2a + 3b a, b 2, 3

9. Identify the variable and constant of each term.
Algebraic Expression Variable/s Constant/s
1. 4y y 4
2. -x x -1
3. 2b3 b 2
4. x – 2y x, y -2
5. 3x - 5 x 3, -5

10. Polynomials
Polynomials are special kinds of algebraic expressions. These
expressions with a restriction that the exponents of a variables must be
whole numbers. A polynomial is a positive integral exponent.
The following are the restrictions of a polynomial:
• 1. No negative and fractional exponent in the variable
• 2. No variable under the radical sign (no variable serves as a
radicand 𝑥)
• 3. No variable in the denominator
2
𝑥

11. Polynomial Not Polynomial
x2
x-2
(the exponent of variable is negative)
y3
𝑦
1
3
(the exponent of the variable is a fraction)
y 4
4 𝑦
(the variable is under the radical sign)
3x
3𝑥
(the variable is under the radical sign)
𝑥
2
2
𝑥
(because the variable is at the denominator)

12. Identify whether is a polynomial or not.
Expression
1. 2x 6. a 2
2. 3xy 7.
2𝑥
𝑦
3. x-3 8. -y
4. x + 2-3 9. x + 3-2
5. a3 - 5 10.
𝑚𝑛
2

13. A. Classifying Polynomials According to
the Number of Terms
• term – an element in a polynomial separated by plus or minus
sign
Example Number of Terms Type of Polynomial
2x one (1) monomial
2a + b2 two (2) binomial
2r – 4s + 2 three (3) trinomial
2x3 + x2 + 5x - 12 more than 3 terms multinomial/polynomial

14. B. Classification of Polynomial According to Degree
– If a polynomial has only one variable, its degree is equal to
the highest power appearing in any of the terms.
– If the polynomial has more than one variable, its degree is
equal to the highest sum of the exponents of the variable in
any of the terms.
–A polynomial of a non-zero constant is considered to be a
polynomial of degree zero. The constant zero is called a
polynomial but without any degree.

15. Example:
Polynomial Degree
2x4 4
3a3 + 4a2
(exponent 3 is higher than exponent 2) 3
xy3
(Exponent 1 in variable x plus exponent 3 in y.
So, 1 + 3 = 4)
4
2a3b2c – bc2
(Exponent 3 in variable a, plus exponent 2 in variable b,
plus exponent 1 in variable c. So, 3 + 2 + 1 = 6)
6
4 0
-2 0