## LESSON 7-2 PROBLEM SOLVING FACTORING BY GCF

Find the GCF of the list of monomials: Notice that in the example below, the first term is x 2 , and x is the only variable present. You can check this by doing the multiplication. Identify the GCF of the polynomial. The following are webpages that can assist you in the topics that were covered on this page: You correctly identified 5 b as a factor of one pair, leaving 2 a and 1, and 4 as the factor of the other pair, also leaving 2 a and 1.

The values 8 and 11 share no common factors, but the GCF of a 6 and a 5 is a 5. It will allow you to check and see if you have an understanding of these types of problems. Factor out the GCF: But the factored form of a four-term polynomial is the product of two binomials. The largest monomial that we can factor out of each term is 2 x. Intermediate Algebra Tutorial Note that this is not in factored form because of the minus sign we have before the 7 in the problem.

The distributive property allows you to factor out common factors.

# Factoring by grouping (article) | Khan Academy

When two or more monomials are combined either added or subtractedthe resulting expression is called a polynomial. Recall that the distributive property of multiplication over addition states that a product of a number and a sum is the same as the sum of the products. You must be able to factor out of every term in order to identify the GCF.

Sometimes, you will encounter polynomials that, despite your best efforts, cannot be factored into the product of two binomials. A whole number, monomial, or polynomial can be expressed as a product of factors.

The two groups 7 x x — 3 and 5 x — 1 do not have any common factors, so this polynomial cannot be factored any further.

## Factoring polynomials by taking a common factor

Rewrite each term as the product of the GCF and the remaining terms. As shown above when we divide 2 x by 2 x we get 1, so we need a 1 as the third term inside of the.

Factor 45 c 2 d 2. Pulling out common factors, you hcf They are the numbers that you can multiply together to produce another number: Factoring is very helpful in simplifying and solving equations using polynomials.

The method remains the same: Note that if you do not factor the greatest common factor at first, you can continue factoring, rather than start all over. Example Problem Find the greatest common factor of and We have to decide which exponent we are going to use. By the time I’m are through with you, you will be a factoring machine.

Factor out 9 c 2 d. Same process, pproblem just have to be careful to look at all the variables. It will allow you to check and see if you have an understanding bby these types of problems.

Practice Lessin 1a – 1d: So the GCF of our variable part is xy. In fact there is no such thing as too much practice.

In this lesson we will study polynomials that can be factored using the Greatest Common Factor. The correct answer is 8 y. The values 8 and 11 share no common factors, but the GCF of a 6 and a 5 is a 5.

# Greatest Common Factor

Factor the common factor 7 x out of the first group. If you vy four terms with no GCF, then try factoring by grouping. Intermediate Algebra Tutorial The greatest common factor GCF for a polynomial is the largest monomial that is a factor of divides each term of the polynomial.

Their solvinv common factor is 10, since 10 is the greatest factor that both numbers have in common. The following are webpages that can assist you in the topics that were covered on this page: But the factored form of a four-term polynomial is the product of two binomials.

## Try Factor a Polynomial by Finding Its Greatest Common Factor

Before we get started, it may be helpful for you to review the Dividing Monomials lesson. Comments We would love to hear what you have to say about this page! This method of factoring only works in some cases.