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### Course: Algebra 2>Unit 3

Lesson 1: Factoring monomials

# Introduction to factoring higher degree polynomials

Unpack the process of factoring monomials in algebra. Learn to simplify third-degree polynomials and tackle fourth-degree monomials. Understand the structure of introductory algebra and apply it to higher degree polynomials. Explore the concept of factoring multiple times and delve into the difference of squares. It's all about breaking down complex expressions into simpler parts!

## Want to join the conversation?

• Good thing he gave these examples. I get way too many people randomly walking up to me and asking me questions like this. Kind of annoying not gonna lie.
• It's difficult to go outside and fearing anybody walking up to me to ask me these stuff.
• Where are the Algebra 1 videos on factoring polynomials? I just need a bit of review...
• You should be able to search it if you cant find it by just looking around. Hope this helps!
• Am I the only one who starts day dreaming halfway through this video of getting a t-shirt printed that says “Hey You! Factor this”?
• Well, 2x = 8, so yes
• if they say don't stress about they mean the opposite of that
• my mathematical career
• So basically we'll be using structure in solving higher degree polynomials instead of deducing logical patterns?
• whts the probability that someones gonna walk up to in the street and ask you "Hey can you factor some complicated math that i dont wanna do?"
• Yes, the chances are slight for somebody to do that but hey, you never know!
However, you are right, this math won't neccesarily help me when Im a mom and trying to figure out how much eggs I should fry. But I just gotta cope with it. Sometimes in life one must to do things that he doesn't want to, so I guess this is a good practice for those times.
Good luck!
• We all must look like mathematicians.
• How come the 7 and 12 turns into 3 & 4? You would need to know what x is wouldn't you?
(1 vote)
• Do you remember factoring quadratic equations? That's what was done here. Might wanna review it if you're unsure!
• do the signs stay the same when factoring polynomails?
(1 vote)
• The signs of the coefficients in a polynomial do not necessarily stay the same when factoring a polynomial. When factoring a polynomial, the goal is to express it as a product of simpler polynomials or factors. These factors can have positive or negative coefficients.

For example, consider the polynomial:

P(x) = 2x^3 - 3x^2 + 6x - 4

When factoring this polynomial, you may find factors like:

P(x) = 2(x^2 - 1) - 3(x^2 - 2)

In this case, the signs of the coefficients within the factors have changed, but this is just a rearrangement of the terms to facilitate factoring. Factoring involves finding common factors and rearranging the terms to express the polynomial as a product of simpler factors. The signs of the coefficients within those factors can change, and that's perfectly fine.

So, in general, the signs of coefficients in a polynomial can change during the factoring process as long as you correctly factor the polynomial into its simpler components.