Mastering Polynomial Operations Review
Algebra 1 - Grade 9 Adding, Subtracting, and Multiplying Polynomials February 10, 2026
Today's Learning Goals
I can add and subtract polynomials I can substitute values into polynomial expressions I can multiply polynomials using the distributive property I can explain my steps and check my work
Essential Question
How do we use polynomial operations to simplify and evaluate expressions correctly?
Bell Ringer: Combine Like Terms
Simplify: 3x² + 5x - 2 + 4x² - 3x + 6 Time: 5 minutes Work independently Show all steps
Bell Ringer Solution
3x² + 5x - 2 + 4x² - 3x + 6 Group like terms: (3x² + 4x²) + (5x - 3x) + (-2 + 6) Combine: 7x² + 2x + 4 Always identify like terms first!
What Are Polynomials?
Expressions with variables and coefficients Terms are added or subtracted Examples: 3x² + 2x - 5, x³ - 4x + 7 Can have one or many terms
Identifying Like Terms
Like terms have the same variable and exponent 3x² and 5x² are like terms 2x and 7x are like terms 3x² and 2x are NOT like terms
Adding Polynomials
{"left":"Align like terms vertically\nAdd coefficients of like terms\nKeep variables and exponents the same","right":"Example: (2x² + 3x + 1) + (x² - 2x + 4)\n= (2x² + x²) + (3x - 2x) + (1 + 4)\n= 3x² + x + 5"}
Practice: Adding Polynomials
Add: (4x² - 3x + 2) + (2x² + 5x - 1) Work with a partner Show your steps Check your answer
Subtracting Polynomials
Distribute the negative sign Change subtraction to addition Example: (3x² + 2x - 1) - (x² - 4x + 3) = (3x² + 2x - 1) + (-x² + 4x - 3) = 2x² + 6x - 4
Quick Check
What happens when we subtract polynomials? Why do we distribute the negative sign?
Substituting Values
Replace variables with given numbers Follow order of operations (PEMDAS) Example: If x = 2, find 3x² - 4x + 1 = 3(2)² - 4(2) + 1 = 12 - 8 + 1 = 5
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