2. Variable – a symbol that represents an unknown
value. Symbols like x, y, a, b, θ, etc. Can be used
as variables.
Constant – is a symbol with exactly one number or
a fixed value in its replacement set. Any number is
a constant such as 7,8, and 11.
Term – each distinct part, together with + and –
signs in an algebraic expression separated by plus
or minus sign.
3. Numerical coefficient – the numerical factor of a term.
Literal coefficient – the variable factor of a term.
Algebraic expression – refers to a constant, a variable, or a
combination of variables and constant involving a finite
number of indicated fundamental operations (addition,
subtraction, multiplication, division, evolution or radicals,
involution or exponents) in algebra.
4. Polynomial – is an algebraic expression that
represents a sum of difference of one or more terms
containing whole-number exponents on the variables.
An expression is NOT a polynomial if:
1. The exponent is a negative number, not a whole
number or a variable.
2. The variable is in the denominator.
3. The variable is under the radical sign.
10. Identify the polynomial and not polynomial. If its not a polynomial change the
expression to make it polynomial.
+ 3x – 4y + 2
- 8 + 2 – x + 4
3. + 3x – 7
+ 4x + 3
- 2y -
12. The degree of a term is the exponent of its variable.
The degree of the polynomial is the highest degree
appearing in any of the terms in that polynomial.
Example: 3 + – 9x + 7, the degree of the terms is as follows: 3 has degree 4,
has degree 2, -9x has degree 1, and 7 has degree 0. Since 4 is the highest
degree, the degree of the polynomial 3 + – 9x + 7 is degree 4.
13. If a term consists of two or more variables, the degree of a term is
the sum of the exponents of the variables.
Example: x + 8 – 3y4, we have the degree of each term as follows:
x has degree 3 (1+2 = 3)
8 has degree 6 (2+4 = 6)
–3y4 has degree 4
since 6 is the highest sum of the exponent from the term, then the
degree is 6.
19. Directions: choose the letter of your answer. Write your answers in a ¼
sheet of paper.
1. It is the highest degree appearing in any of the terms in that polynomial.
A. Degree
B. degree of a term
C. sum of the exponents
D. degree of a polynomial
2. what is the degree of the polynomial expression , 4 + 3 + 5 - yx – 8?
A. 5 C. 7
B. 6 D. 8
20. 3. What is the degree of the polynomial expression , 9 + 2x.
A. 9 C. 4
B. 5 D. 2
4. What is the degree of the polynomial expression, 3 + 2 + 8 - 4x4y –
?
A. 5 C. 8
B. 6 D. 9
5. What is the degree of the polynomial? 9 + 2 - + 9 – 2
A. 5 C. 2
B. 9 D. 4
21. The degree of a term is the exponent of its variable.
The degree of the polynomial is the highest degree
appearing in any of the terms in that polynomial.
If a term consists of two or more variables, the
degree of a term is the sum of the exponents of the
variables.
22. EXAMPLE: 3 + – 9X + 7, THE DEGREE OF THE TERMS IS AS
FOLLOWS: 3 HAS DEGREE 4, HAS DEGREE 2, -9X HAS
DEGREE 1, AND 7 HAS DEGREE 0. SINCE 4 IS THE HIGHEST
DEGREE, THE DEGREE OF THE POLYNOMIAL 3 + – 9X + 7 IS
DEGREE 4.
23. EXAMPLE: X + 8 – 3Y4, WE HAVE THE DEGREE OF EACH
TERM AS FOLLOWS:
X HAS DEGREE 3 (1+2 = 3)
8 HAS DEGREE 6 (2+4 = 6)
–3Y4 HAS DEGREE 4
24. KIND OF POLYNOMIAL ACCORDING TO THE NUMBER OF TERMS
Number of
Terms
Kind of
Polynomial
Examples
1 Monomial x , 5y , 6c
2 Binomial a+b , 2x-y, 3-3, 2(x+y),
by distributive: 2(x+y) = 2x+2y
𝑖𝑠 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑡𝑜 +
3 Trinomial a+b+c, 2(x + y + z)
by distributive:
2(x+y+z) = 2x+2y+2z
4 or more Multinomial + 5 – 4x + 5
25. IDENTIFY THE FOLLOWING THE
KIND OF POLYNOMIAL.
1. 20a
2. 11b – 60a
3. 80x + 76y – 3c
4. 98a – 34b – 90x + 5
5. 55 (a – b)
26. KINDS OF POLYNOMIALS ACCORDING TO ITS DEGREE
Kind of Polynomials
in
terms of Degree
Degree Examples
Constant 0 1,5 or any number
Linear 1 2x, x+1, 3x-2y+3
Quadratic 2 2, -1, 3-2y+3
27. IDENTIFY THE FOLLOWING THE KIND OF
POLYNOMIALS IN TERMS OF DEGREE.
1. 100
2. 21a + 4b
3. 34
4. – 5b
5.− 10
28. TRANSLATING VERBAL PHRASES TO ALGEBRAIC EXPRESSION
Verbal Phrases Algebraic
Expression
Verbal
Phrases
Algebraic
Expression
the sum of m and 8 m + 8 10 added to c c + 10
the difference of m
and 8
m – 8 10 subtracted from c c - 10
7 plus a 7 + a 7 minus a 7 – a
5 more than t t + 5 5 less than t t - 5
q increased by p q + p q decreased by p q - p
11 greater than n n + 11 9 take way d 9 - d
exceeds r by twenty r + 20 18 reduced by n 18 – n
29. the product of
8 and m
8m The quotient of
8 and m
10 times c 10c 10 divided by c
twice x 2x The ratio of 7
to a
One – half of p p p slit into 4
equal parts
7 multiplied by
b
7b x divided into
10
30. Activity : Find a match!
Your task is to pair each verbal phrases on the box with its corresponding number. Each number corresponds to a letter, which, when correctly matched, with
reveal a quotation.
_
____1. The sum of a number and three.
_____2. A difference of four times a number and one.
_____3. Four times a certain number decreased by one.
_____4. A certain number decreased by two.
_____5. The difference of two and a number.
A - x + 3 L- 4x – 1 Q- 2 - x
B- 3 + 4x U- 4x + 3 M- x - 2
