# Products and Factoring

Understanding Factors and Products

When multiplying two or more numbers together the result obtained is called product. Therefore, any numbers once multiplied are called: factors of the product.

Example 1

3 , a , x can be considered as factors to product 3ax.

Example 2

4, y, x can also be considered as factors to product 4yx

It is also very important to understand that in order to find the product of a monomial and a polynomial, multiply the monomial by each and every term of the polynomial.

Therefore, if you have 2(3a + 4b)

Thus, the answer is: 6a + 8b

Two factors of any numbers are 1 and itself.

Let's take 1 and 31.

They are factor of 31, meanwhile 1 and x are factors of x.

A prime number is a natural number whose only divisors bigger than 1 are 1 and itself.

Example: 3, 5, 7, 13, and 17 are prime numbers.

Products can be divided into factors or into prime factors.

For example, let's take number 36(product) = 4 . 9 (factors) = 2.2.3.3 (prime factors). Therefore, to factor a number or expression is to find its factors, not including 1 and itself.

Thus, 4ax + 8a may be factored into 4(ax + 2a), or further 4a( x + 2).

To factor a polynomial completely,continue the process of factoring until the polynomial factors cannot be factored no more.

Example, 4ax + 8a may be factored completely into 4a(x + 2)

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Factoring

It is the process of separating, or resolving, a quantity into factors. For we say that the product of 4 and 6 is 24. This 24 can be factored as the product of (4)(6). In all, we are combining the numbers, while the process of factoring breaks down the given expression into smaller multiplicative units or factors.

Hang in there these lessons are tailored for you, students. And soon, you will see yourself doing many things such as: