Adding and Subtracting Polynomials

Objectives

• At the end of the lesson, the students should be able to: - identify the types of polynomial - add and subtract polynomials - apply steps in adding and subtracting polynomials to simplify an expression

POLYNOMIAL
- a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx²).
Example:
6
3x+1
4x2+1x+1
6x3+4x3+3x+1
6x4+3x3+3x2+2x+1

Types of Polynomial

MONOMIAL
- a monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term.

Example:
5x
3
6a
-3xy

BINOMIAL
- is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.

Example:
– 5x + 3
6a^4 + 17x
xy^2 + xy

TRINOMIAL
- is an expression which is composed of exactly three terms.

Example:
– 8a^4+2x+7
4x^2 + 9x + 7

Try it!
Identify the types of polynomial of the following mathematical expressions.
1. 3x2 – 2x + 6
2. x3-2x
3. 3y
4. x^2+2x+20
5. 3x+5

Steps for Adding and Subtracting Polynomials

STEP 1
Remove all parentheses. When adding, distribute the positive (or addition) sign, which does not change any of the signs. When subtracting, distribute the negative (or subtraction) sign, which changes each sign after the subtraction sign.

STEP 2
Combine like terms. Remember that to combine like terms the variable and the power of each variable must be exactly the same.

Example 1.

Simplify: (3x^3– 5x + 9) + (6x^3 + 8x – 7)

Step 1: Remove all parentheses.
3x^3– 5x + 9
+ 6x^3 + 8x – 7
Step 2: Combine like terms.
9x^3 + 3x + 2

Example 2.

Simplify: (–3x^2 + 9xy – 5y^2) – (4x^2 + 7xy – 8y^2)

Step 1: Remove all parentheses.
- 3x^2 + 9xy - 5y^2
- 4x^2 - 7xy + 8y^2
Step 2: Combine like terms.
- 7x^2 + 2xy + 3y^2

Exercise!
Add or subtract the following polynomials.
1. (5x^4-3x^2+4) + (6x^3-4x^2-7)
2. (5x^3-7x^2+3x-4) - (8x^3+2x^2+3x-7)
3. (6x^2–7x+4) - (7x^2–9x+8)
4. (2x^2y–5xy + 3y^2) – (7xy-6y^2+5x^2y)
5. (4x^3–5x–8) - (6x^2–3x+8)

Prepared by:
John Ivan A. Cervantes
BSED - 3D