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## Algebra (all content)

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

Lesson 10: Introduction to factorization

# 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.
• Why did he put 10x at ??
(1 vote)
• When you multiply (x+3)(x+7), you would get x squared plus 7x plus 3x plus 21. You have 3x and 7x, which add together to get 10x.
• What exactly is the purpose of factorizing something?
• i dont understand
• we know that
(a+b)(a-b)=a^2-b^2

This means that,
a+b is a factor of a^2-b^2, ALSO
a^2-b^2 is divisible by a+b

but dividing a^2-b^2 by a+b does not give a-b

plz help me to understand this concept in term of this formula

THANK YOU.
(1 vote)
• Look, if a=1&b=2, a^2-b^2=-3, and -3/a+b=-3/3=-1, a-b=-1, so (a^2-b^2)/(a+b)=a-b. (Replace unknowns with numbers)
• 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.
• what is the difference between polynomials, and binomials?
• A polynomial is simply a fancy word to describe a math statement with several terms. A mononomial is the opposite - it is a statement with only one term. A binomial is a type of polynomial that contains exactly two terms. All of these are pretty simple to remember because they use the same Greek/Latin roots that many other math terms use. (Poly means many, mono means one, and bi means two). Here are some examples of all of these concepts.

Polynomial:
- 4x^2 + 5x + 6
- x + a + c
- 433 + 19b + 17c + 25a

Mononomial:
- 5x
- a
- 19
- 7

Binomial:
- x + 7
- 4x + 9
- 9a + b

Hope that helps!
(1 vote)
• Is not (3xy)(-2x^2y^3) the same as [(xy) + (xy) + (xy)][(-x^2y^3) + (-x^2y^3)] ?