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# Terms, factors, & coefficients

In math expressions, terms are the components added or subtracted, factors are the elements multiplied within each term, and coefficients are the numbers multiplying variables. Understanding these concepts is crucial for effective communication and problem-solving in mathematics. Created by Sal Khan.

## Want to join the conversation?

• Why is the coefficient so important?
• Sometimes, when an equation like 4x+4=0 pops up, it would be easy to write it like this: 4(x+1)=0 to find x. Though it might not seem important right now, coefficients can help simplify an equation. To me, it seems that the coefficient would be most useful when finding the value of a variable using factorization. I do not know many other ways a coefficient would be used but it is still important.
Edit: Also, like 6x, it's a big pain to writing it x*6 every time, so it's more practical and neater, helping organizing your equations so you don't mess up!
• define interger
• An integer means a whole number or a negative number, as long as it isn't a fraction or a decimal.
• Can someone clarify what a factor is?
• here's a song my teacher made up wich is really helpful for remembering factors,"factors are the numbers that you multiply to get the product."
• Hey, I really need help with coefficients, they're hard to understand.
• I will try my best to have this make sense:
coefficients are the number when you multiply a number and a variable. For example 5a the coefficient in that term is 5 if you have 48e the coefficient is 48. So the coefficient is the number when you multiply a number times a variable.

I hope this helps!!😀
• What of Constants? Or are "Terms" constants?
• It's more like the other way around. A constant is something like '5', where it won't be affected because of variables. A term can be a constant, but not always is. A constant, however, can be a term. :)
• im confused about in the video he says xy is the same as 1 times x y but i thought variable din't have a fixed value also some of the things he is saying like we already learned it does he explain in future videos?
this feels like a huge leap from the last unit
• While variables don’t have any fixed values, it is still true that 1xy is always equal to xy, no matter what values are used for x and y. This is because 1 times any number is always that number (multiplicative identity property).

When you learn how to simplify algebraic expressions, you will see many situations with two algebraic expressions equal to each other, for all possible values of the variables. Such expressions are called algebraically equivalent. A statement of algebraic equivalence is called an algebraic identity. Other examples of algebraic identities are shown below (for all values of the variables):

2x + 3x = 5x
8x - 6x = 2x
2(x + y) = 2x + 2y
3(x + 4) = 3x + 12
x + y - x = y
x - (y + z) = x - y - z
and many more!
• Can someone explain the coefficient in simple term please.
• A coefficient is a number multiplied by a variable.
Examples of coefficients:
In the term 14c, the coefficient is 14.
In the term g, the coefficient is 1

Hope that helps.