Addition and Subtraction of Polynomials
Objectives
Start
Story
Introduction to Polynomials
Adding Polynomials
Subtracting Polynomials
Summary
Story
Introduction to Polynomials
What is a Polynomial?
Definition: A polynomial is any algebraic expression formed by addition, subtraction, multiplication or division of natural powers of variables and coefficients
Example 2:
Example 1:
is NOT a polynomial, because the expression has a quotient of variables and a fractional power of x (1/2).
is a polynomial, because the expression is a sum of powers of x with coefficients 2, 2, 0.
Try it by yourself:
Adding Polynomials
Addition of polynomials can be done horizontally or vertically.
Addition of Polynomials Vertically
Combine like terms (terms with the same variable raised to the same power).
Example 1:
Add
Example 2: Add
x²-3y² + 3xy+3x
5x² + 5x + 5
Adding Horizontally.
Combine like terms (terms with the same variable raised to the same power).
Example 2:
Add
Example 1: Add
4x⁴+3x²+7x+1
7x²-x-9
Subtracting Polynomials
Subtraction of Polynomials
Combine like terms (terms with the same variable raised to the same power).
Example 2: Subtract vertically:
Example 1:
Subtract horizontally:
x²-8x-11
x²-x-3
Let's see some examples:
A rectangular garden is represented by the polynomial 4x² + 6x. Another garden is represented by 2x² + 3x.
What is their combined area?
A=6x²+9x
Try it by yourself:
Summary: Polynomials
+, -, x or ÷ of natural ()ⁿ of variables and coefficients
SUBTRACTION
ADDITION
PERFORMED using
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
9TH-ADDITION-AND-SUBTRACTION-OF-POLYNOMIALS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.AR.2: Write, solve and graph linear equations, functions and inequalities in one and two variables. MA.912.AR.2.1 Given a real-world context, write and solve one-variable multi-step linear equations. MA.912.AR.2.2 Write a linear two-variable equation to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context. ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.
MATERIAL
It is highly advised to have:
- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
WEEK 10-ADDITION-AND-SUBTRACTION-OF-POLYNOMIALS
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Transcript
Addition and Subtraction of Polynomials
Objectives
Start
Story
Introduction to Polynomials
Adding Polynomials
Subtracting Polynomials
Summary
Story
Introduction to Polynomials
What is a Polynomial?
Definition: A polynomial is any algebraic expression formed by addition, subtraction, multiplication or division of natural powers of variables and coefficients
Example 2:
Example 1:
is NOT a polynomial, because the expression has a quotient of variables and a fractional power of x (1/2).
is a polynomial, because the expression is a sum of powers of x with coefficients 2, 2, 0.
Try it by yourself:
Adding Polynomials
Addition of polynomials can be done horizontally or vertically.
Addition of Polynomials Vertically
Combine like terms (terms with the same variable raised to the same power).
Example 1: Add
Example 2: Add
x²-3y² + 3xy+3x
5x² + 5x + 5
Adding Horizontally.
Combine like terms (terms with the same variable raised to the same power).
Example 2: Add
Example 1: Add
4x⁴+3x²+7x+1
7x²-x-9
Subtracting Polynomials
Subtraction of Polynomials
Combine like terms (terms with the same variable raised to the same power).
Example 2: Subtract vertically:
Example 1: Subtract horizontally:
x²-8x-11
x²-x-3
Let's see some examples:
A rectangular garden is represented by the polynomial 4x² + 6x. Another garden is represented by 2x² + 3x.
What is their combined area?
A=6x²+9x
Try it by yourself:
Summary: Polynomials
+, -, x or ÷ of natural ()ⁿ of variables and coefficients
SUBTRACTION
ADDITION
PERFORMED using
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
9TH-ADDITION-AND-SUBTRACTION-OF-POLYNOMIALS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.AR.2: Write, solve and graph linear equations, functions and inequalities in one and two variables. MA.912.AR.2.1 Given a real-world context, write and solve one-variable multi-step linear equations. MA.912.AR.2.2 Write a linear two-variable equation to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context. ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.
MATERIAL
It is highly advised to have: