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### Course: Algebra (all content)>Unit 10

Lesson 1: Intro to polynomials

# Simplifying polynomials

Simplifying the polynomial 3x²-8x+7+2x³-x²+8x-3 by combining like terms. Created by Sal Khan.

## Want to join the conversation?

• at when sal talks about being redundant what exactly does he mean?
• Redundant means repetitive (If you say the same thing over and over, you're being redundant.)
Hope that helps.
• Could factoring be considered a part of the simplifying process? Because all the terms at the end are divisible by 2 which could give us:
2x^3 + 2x^2 + 4
2(x^3 + x^2 + 2)
• Yes, that would be perfectly legitimate.
• is there anyway i can practice this?
• Hi!
• How can you be sure that something cannot be simplified further?
• When you see that there no more like terms and every term is different.
• If a problem like this is already arranged with the highest terms to lowest terms, would my answer change if I mix the numbers around like what he did in the video? Because if so, then it becomes easier for me to understand what operation(+-) to use on each term. This probably makes no sense
• I don't think it matters too much, unless you're factoring. I'm pretty sure you can arrange the terms any way you'd like, however, most teachers want you to put the polynomial in standard form (highest to lowest degree)
• Sal said that we finished simplifying the polynomial but can't we group the 2x^3 and 2x^2 as 2x^2 (x +1) ?
• If you were asked to simplify the polynomial, you should have a list of all unlike term like shown in the video: 2x^3 + 2x^2 + 4.

You would not change it into: 2s^2 (x + 1) +4 for 2 reasons:
1) Factored form is not simplified form.
2) Even if asked for factored form, you would not factor only 2 out of 3 terms. You would need to factor a common factor from all 3 terms.

Hope this helps.
• *what does sal mean when he says highest degree at ?*
• The highest degree means the highest powers among different terms of that polynomial.
Hope you understand...
• how do you do that with fractions
• weird. during some point in the video, it said x^2+x^3 can not be simplified.
• Aiden,

That statement is correct. You cannot add variables of different degrees.
• Remember, `x` is the same as `1x`. And, in this problem, `x²` means `1x²`
So, `3x² - x²` means `3x² - 1x²`
Thus, `3x² - 1x²` = `2x²`