Algebra – Factoring and Problem Solving by Factor

In this lesson we will learn:

1. Factoring by dividing
2. Prime number
3. Relatively prime
4. Solving the greatest common factor (GCF) of natural numbers
5. Determine the GCF of monomials
6. Factor out the GCF of a polynomial
7. Factor a four-term polynomial by grouping
8. Euclid's algorithm
9. Multiples factoring
10. Least common multiple

Learning out come:

- Factors, dividing by a factor always gives you a whole number
- Prime numbers, their only factors are 1 and themselves
- Factoring out, pulling out common factors using the distributive law
- Factoring out negatives, flip the signs when you factor out negative numbers
- Greatest common factor, the biggest factor that numbers have in common
- Relatively prime, when two numbers have no common factors
- Euclid's algorithm, a 2000-year-old way to calculate the GCF
- Multiples, what you get when you multiply numbers by integers
- Least common multiple, the smallest multiple numbers have in common

We can find greatest common factor (GCF) collection of natural numbers by, first thing we need to find the prime factorization of each because GCF is the product of all the common prime factors.

Please remember that the greatest common factor or simply GCF of two or more monomials is the product of the GCF of the coefficients and the common variable factors with the smallest power.

When the terms of a polynomial have a greatest common factor (GCF), then we can factor out that GCF using the distributive its property and divide each term of the polynomial by the GCF to determine the terms of the remaining factor.

In some case, four-term polynomials can be factored by grouping the first two terms and the last two terms and then, factor out the GCF of each group, finally factor out the common binomial factor.

To factoring by grouping, sometimes we have to rearrange the terms to find a common binomial factor, and after factoring out the GCF then, the remaining binomial factors must be the same for the technique to work.

Please notice that not all polynomials can be factored as the product of polynomials with integer coefficients. however, we called it as a prime polynomial.

Here something to remember:

Saying a number is even is the same as saying number 2 is a factor.

Prime number has only positive factors are 1 and the number itself. The smallest prime number is number 2, the number 1 itself not prime.

Composite has factors other than 1 and the number itself. Factoring out or pulling out common factors by using the distributive law.

Factoring out negatives, flip the signs when you factor out negative numbers. Flip the signs when you distribute a negative.

Greatest common factor is the biggest factor that numbers have in common. Common factors are factoring that numbers have in common. 

Composite has factors other than 1 and the number itself. Greatest common factor is the biggest factor that numbers have in common.

Common factors are factoring that numbers have in common. 

Relatively prime are when two numbers have no common factors or when their greatest common factor is 1. 

Relative prime we also can called Coprime. Using Euclid's algorithm to finding the greatest common factor (GCF). 

Keep replacing the bigger number with the difference until the number are equal then that’s the GCF.

Multiplying a number by an integer gives you a multiple of that number. 

Common multiple are positive multiples numbers have in common. Least common multiple are the smallest multiple numbers have in common 

Algebra I – Factoring – Part 01:

Algebra I – Factoring – Part 02: