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### Course: Integrated math 2>Unit 2

Lesson 4: Introduction to factoring

# Intro to factors & divisibility

Sal explains what it means for a polynomial to be a factor of another polynomial, and what it means for a polynomial to be divisible by another polynomial.

## Want to join the conversation?

• But how did he get 10x in the first place? In the first problem, he only multiplied the similar terms (3 times -2, x times x etc.) But in the second one he multiplied everything
• When multiplying binomials, think of it as doing the distributive property. Multiply each term by each term. So x * x = x^2, while 3 * 7 = 21. But, x * 7 =7x, while 3 * x = 3x. So, x^2 +7x + 3x + 21. Simplifying that, you add the 3x to the 7x to equal 10x. The final answer is, x^2 + 10x + 21
• Hi,
Just to get some clarity,
What is the difference between binomial, polynomial, trinomial, etc?
• A monomial is a polynomial with 1 term.
A binomial is a polynomial with 2 terms.
A trinomial is a polynomial with 3 terms.
• can decimals be factors or is it just integers? as an example, you can definitely say that 3 is a factor of 6, but can you say that 2.5 is a factor of 5?
• Great question! When we talk about factors of whole numbers, we are looking for whole numbers. 2.5 is not a whole number, so it is not a factor of 5. Negative integers, like -1 and -5, are not factors either, because they are not whole numbers. The only factors of 5 are 1 and 5, making 5 prime.
• Is there a different method for this problem?
• Not that I know of... it would probably be best to use this method until you learn/are taught a different method at a later stage of your education.
• What exactly is the purpose of factorizing something?
• so is 12 a factor of 12?
• Yes, 12 is a factor of 12. This is because 1x12 = 12.
Factors are numbers that multiply to create another number.
The list of factors for 12 are: 1, 2, 3, 4, 6, and 12.
• Is not (3xy)(-2x^2y^3) the same as [(xy) + (xy) + (xy)][(-x^2y^3) + (-x^2y^3)] ?
• Yes, but why do you want / need to write the expression that way? This is rarely done.
• If x^2 + 10x + 21 is a trinomial, then is x^2 + 3x + 7x + 21 a quadrinomial, or still a trinomial, since it can be simplified to the former?
• In its expanded form, it is a quadrinomial because it has 4 terms at that point. However, it is still a quadratic expression.