What Is Factoring?
Question
Factoring is the process of writing an integer or mathematical expression as
Hi, my name is Bassem Saad. I'm an associate math instructor and a Ph.D. candidate, and I'm here today for About.com to answer the question:
What Is Factoring?

So, factoring is the process of writing an integer or mathematical expression as a product of terms. So in arithmetic, we can use factoring to factor integers into primes. Say 75, we can factor it into five, times five, times three. Once we know how to factor integers into their primes, we can use this to find the least common denominator to sum our fractions.
Factoring

So let's take the fraction one-sixth, plus one-tenth. We factor the denominator of one-sixth into two, times three, and we factor ten into two, times five. From this, we can find our least common denominator, by taking two for each of the denominators. So you only have one two, times one three for the first term, and one five for the second term. That means our least common denominator is 30. So we want the denominator of both these fractions to equal 30, so we have to multiply the denominator of the first fraction by five, but that means we also have to multiply the numerator by five. So one, times five is five; six, times five is 30. And now for the next fraction, one-tenth, we have to multiply the denominator by three to get 30, and that means we have to multiply the numerator by three to keep the fraction the same. So we have three over 30.
Common Denominators in Factoring

So now that we have a common denominator, we only need to add our numerators. So five, plus three is eight, so our new fraction is eight over 30. We can factor a two out of the eight and the 30, and cancel the two out, leaving us with a simplified fraction of four over 15. In algebra, we usually see factoring when we're trying to factor a polynomial.

A lot of times we're given a polynomial, in this case a binomial, and we can factor it into a product of two other binomials. Notice in this form, we can see what the roots of this polynomial is very clearly. If x equals two, this side of the equation will equal zero, which means that when we plug two into x, this side of the equation must equal zero too. When x equals minus two, it's also true that the right side of the equation will equal zero, and thus, when we plug in negative two into the left side, the left side of the equation must also equal zero. So now we know what factoring is.