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Factors

As we start to get into division, we''ll start hearing the word "factors" very often. But what exactly is a factor? how is this concept related to division? What do we need to know about factors? Let''s find out:

Factors defined

Factors are like smaller building blocks of numbers. When we multiply them, we get the original number that we broke down into smaller parts.

For example, 5 is a factor of 10, since we can multiply 5 by 2 to get 10. But 2 is also a factor of 10 since we can multiply 2 by 5 to get 10.

Aside from 1 and 10, there are no other factors for the number 10. We can''t use numbers like 3.33 and 3 because factors must be a whole number.

What about polynomials?

The term "factor" takes on a slightly more complex meaning when we''re dealing with polynomials.

Consider the following:

x+1
is a factor of
x2-2x-3


Why?

Because we can do this:
(x+1)(x-3) = x2-2x-3


In other words,
x+1
is a smaller piece of the larger polynomial equation, and when it is multiplied by another polynomial
(x-3)
, it results in the original polynomial
x^2-2x-3

Common factors

Common factors can be very important in math.

We can look at two different numbers and determine if they have common factors. For example:

4x+4
and
x2-2x-3
have x+1 as a common factor.
4x+4= 4(x+1)


and
x2-2x-3 =(x+1)(x-3)

Topics related to the Factors

Advanced Factoring

Irreducible Polynomials

Factoring: a ≠ 1

Flashcards covering the Factors

4th Grade Math Flashcards

Common Core: 4th Grade Math Flashcards

Practice tests covering the Factors

Common Core: 4th Grade Math Diagnostic Tests

4th Grade Math Practice Tests

Connect your student with a qualified tutor who understands factors

Understanding factors is critical for early math students, and a tutor can help them develop a solid foundation of knowledge with fun, engaging, and targeted teaching methods. Varsity Tutors helps students of all ability levels, and we''ll connect your student with the right tutor.

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