2. Definition of Terms
POLYNOMIAL
β’ Is an algebraic expression that represent a sum of one or more terms
containing whole number and exponents on the variables.
MONOMIAL
β’ It is a polynomial with only one term. E.g., 2x, 3π₯2
, 2, ab, 42xyz
BINOMIAL
β’ It is a polynomial with two terms. E.g., 2x + 7, 3π2+ a, 4xz + 2yd
TRINOMIAL
β’ It is a polynomial with three terms. E.g., a + b + c, 2π₯2
+ 3y + 6, 2x + 2xy +
4y
5. β’You can only combine terms together if they
are LIKE TERMS.
β’If they are not like terms, you must keep
them separate.
6. 2x + 3y + 4x
Let x be a circle, and y be a triangle.
2x + 3y + 4x
= 6x + 3y
7. ADDITION OF POLYNOMIALS
To add like terms together, you add the coefficients and
keep the variable part the same.
4x + 3x = 7x
Add the
coefficients.
The variable part
stays the same.
8. ADDITION OF POLYNOMIALS
There are two (2) common methods by which we add
algebraic expressions.
For example:
(7xy + 5yz β 3xz) + (4yz + 9xz β 4y) + (-2xy β 3xz + 5x)
10. METHOD 2
In horizontal form, use the Associative and Commutative
Properties to regroup and combine like terms.
(7xy + 5yz β 3xz) + (4yz + 9xz β 4y) + (-2xy β 3xz + 5x)
= (7xy β 2xy) + (5yz + 4yz) + (-3xz + 9xz β 3xz) + 5x β 4y
= 5xy + 9yz + 3xz + 5x β 4y
11. Example 1: Adding Polynomials
A. (4π2+ 5) + (π2 - m + 6)
= (4π2+ 5) + (π2 - m + 6) Identify like terms
= (4π2+ π2) + (-m) + (5 + 6) Group like terms together
= 5ππ - m + 11 Combine like terms
B. (10xy + x) + (-3xy + y)
= (10xy + x) + (-3xy + y) Identify like terms
= (10xy β 3xy) + x + y Group like terms together
= 7xy + x + y Combine like terms
14. SUBTRACTION OF POLYNOMIALS
To subtract polynomials, remember that subtracting is the same as
adding the opposite. To find the opposite of a polynomial, you
must write the opposite of each term in the polynomial:
For example:
- (2 π₯3
- 3x + 7) = -2 π₯3
+ 3x - 7
15. Example 1: Subtracting Polynomials
Subtract.
= (π₯3
+ 4y) β (2 π₯3
)
= (π₯3 + 4y) + (-2 π₯3) Rewrite the subtraction as
addition of the opposite
= (π₯3 + 4y) + (-2 π₯3) Identify like terms
= (π₯3 - 2 π₯3) + 4y Group like terms together
= - ππ
+ 4y Combine like terms
16. Example 2: Subtracting Polynomials
Subtract.
= (7π4
- 2π2
) β (5π4
- 5π2
+ 8)
= (7π4 - 2π2) + (-5π4 + 5π2 - 8) Rewrite the subtraction as
addition of the opposite
= (7π4 - 2π2) + (-5π4 + 5π2 - 8) Identify like terms
= (7π4 - 5π4) + (-2π2 + 5π2) - 8 Group like terms together
= 2ππ
+ 3 ππ
- 8 Combine like terms
17. Example 3: Subtracting Polynomials
Subtract.
= (-10π₯2
- 3x + 7) β (π₯2
- 9)
= (-10π₯2 - 3x + 7) + (-π₯2 + 9) Rewrite the subtraction as
addition of the opposite
= (-10π₯2 - 3x + 7) + (-π₯2 + 9) Identify like terms
-10π₯2 - 3x + 7 Use the vertical method.
-π₯2 + 0x + 9 Write 0x as a placeholder.
-11ππ - 3x + 16 Combine like terms