### LESSON 7-2 PROBLEM SOLVING FACTORING BY GCF

C a 5 a — 1 Incorrect. Factor out the 5 b 2. To factor a polynomial, first identify the greatest common factor of the terms. The process of breaking a number down into its prime factors is called prime factorization. A whole number, monomial, or polynomial can be expressed as a product of factors. You must be able to factor out of every term in order to identify the GCF. Factor out a GCF from each separate binomial.

B 8 y Correct. To be in factored form, it must be written as a product of factors. Group the first two terms together and then the last two terms together. So our numerical GCF is 3. Hence our GCF is.

You can use some of the same logic that you apply to factoring integers to factoring polynomials. There are several methods that can be used when factoring polynomials. Math works just like anything else, if you want to get good at it, then you need to practice it.

# Factoring Polynomials Using the GCF

This process is basically the reverse of the distributive property found in Tutorial 5: After completing this tutorial, you should be able to: If you can find common factors for each term of the polynomial, then gc can factor the polynomial. Example Problem Find the greatest common factor of 25 b 3 and 10 b 2.

Factor out 9 c 2 d.

So you can factor out a 5 and rewrite the polynomial as a 5 8 a — Example Problem Find the greatest common factor of 81 c 3 d and 45 c 2 d 2. To factor a polynomial, first identify the proboem common factor of the terms, and then apply the distributive property to rewrite the expression.

Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument. It will allow you to check and see if you have an understanding of these types of problems. You can check this by doing the multiplication. When you factor a polynomial, you are trying to find probelm quantities that you multiply together in order to create the polynomial.

Factor out the common binomial. To factor a polynomial, first identify the greatest common factor of the terms. The values 8 and 11 share no common factors, but the GCF of a 6 and a 5 is a 5. D 8 xy 3 Incorrect. Factor the common factor, xout of factoeing first group and the common factor, 4, out of the second group. The polynomial is now factored. Remember, all polynomial problems will not have a GCF, and we will discover in the next few lessons how to factor if there is no GCF.

Answer Cannot be factored.

## Factoring polynomials by taking a common factor

Find the greatest common factor of 25 b 3 and 10 b 2. Something to look forward to!

If we use the exponent 8, we are in trouble. Note that if we multiply our answer out, we do get the original polynomial. Bu a polynomial with four terms by grouping. Find the GCF of the second pair of terms. It looks like each term has an x and a y. 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. Factors are the building blocks of multiplication.

In the next two tutorials we will add on other types of factoring. Divide the GCF out of every term of the polynomial. Factoring gives you another way to write the expression so it will be equivalent to the original problem.