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### Course: Algebra 2>Unit 3

Lesson 6: Polynomial identities

# Polynomial identities introduction

Polynomial identities are equal expressions involving polynomials. We can prove these identities through algebraic manipulation, like expanding and simplifying. This helps us see if two expressions are the same for all values of a variable, making them true polynomial identities.

## Want to join the conversation?

• Am I the only one that finds it funny that people on the street walk up to Sal and ask him random polynomial questions?
• is it just me or do a lot of people just come walkin up to sal and say 'hey you factor this?'
• these people on the street need to mind their business
• I know right! They're just asking questions they themselves are unable to answer, making us tryna crack our brains.
• I am a bit confused here. I came up with two after working my way through the second example. If I entered two as (n) it would make the polynomial even on both sides. Wouldn't that make the second example an identity?
• A polynomial identity is when it is equal for ALL values of n
• Tell me if my definition of a mathematical identity is correct: an equality between two expressions in which they are not the same but, upon manipulating one or the other or both, they can be the same.
• You have to be careful about using phrases like "the same" in math. You need to be very precise in math for good reasons. If two expressions are equal, that means they are always "the same." They might look different, but an identity can be expressed as an equation which is always true. For example 5 + 1 = 4 + 2.
• what is a Polynomial identity
• A polynomial identity is an equation involving polynomials that is always true.
For example, this is a polynomial identity:
(x+1)^2 = x^2+2x+1. No matter what x is, both sides are always equal.

You can verify a polynomial identity if you can rewrite one side to look exactly the same as the other side.

Hope this helps!
• Is there a real-world purpose to this concept? I tend to retain this type of information better if I know how it is used in the world.
(1 vote)
• One example I can think of is that polynomial identities are used to find variable(s) to find where to support a curve in a bridge or building for an engineer. Statistics in graphs could also use polynomials in general to find trends in stocks or other economic related topics.
• Where'd the 6n come from?? Wouldn't it just be n^2 + 9?
• (𝑛 + 3)² = (𝑛 + 3)(𝑛 + 3)
Using the distributive property twice, aka "FOIL",
we get 𝑛² + 3𝑛 + 3𝑛 + 9, which simplifies to 𝑛² + 6𝑛 + 9