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### Course: Grade 8 math (FL B.E.S.T.)>Unit 1

Lesson 2: Factoring monomials

# 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.
• What exactly is the purpose of factorizing something?
• 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.
• 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.
• 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.
• Would 1/2 and 20 be factors of 10? Could fractions and decimals be defined as factors? It doesn't specify if the factors must be whole numbers or integers. Also, if you have 3xy for example, and you say that 6xy^2 is a factor of it, would that be wrong? If so, is it because a monomial cannot have a fractional coefficient or is it because factors cannot be decimals or fractions?
(1 vote)
• Factors are integers that will divide evenly into a number without leaving a remainder. 1/2 would not be considered a factor of 10 as it is not an integer. 20 would not be a factor of 10 because it does not divide evenly into 10.