Polynomials-Target+C-Factoring+GCF-Guided+Learning


 * Polynomials Target C: Factor a GCF (constant and variable with a degree of 1)**

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 * [[image:Discuss this.png width="208" height="116"]] || Find a reason why each one doesn't belong.

As you may recall from your previous math experiences, GCF stands for Greatest Common Factor. A common factor is a factor that two numbers are both divisible by. Let's take a look at the factors of 12 and 18. Here are the factors of 12: 1, 2, 3, 4, 6, and 12. What are the factors of 18? They are: 1, 2, 3, 6, 9, and 18. So you can see that 2, 3, and 6 are common factors of 12 and 18 because both 12 and 18 are divisible by 2, 3, and 6. Out of those factors, we can see that 6 is the GCF between 12 and 18 because it is the greatest out of all the common factors. Is it coming back to you?

What happens though if we incorporate a variable? What would be the GCF between 16x 5 and 24x 2 ? Sometimes it helps to look at each polynomial expression in two parts: 1) identifying the GCF of the coefficients and 2) identifying the GCF of the variables. The GCF of 16 and 24 is 8 because 8 is the greatest number they are both divisible by. To determine the GCF of the variables, it is still based on what each polynomial is divisible by, which can be found using the variable with the lowest degree. 16x 5 has an exponent of 5, and 24x 2 has an exponent of 2. For the GCF we want to use the expression with the lowest degree that is a factor of each polynomial which is x 2. So the GCF for 16x 5 and 24x 2 would be 8x 2. What would be the GCF of 30x 4 and 25x 7 ? That's right! It would be 5x 4 because 5 is the GCF of 30 and 25, and x 4 is the variable expression that has the lower degree. Now let's take a look at how the GCF applies to our polynomials.


 * Important: When the leading coefficient is negative, you need to factor out the negative with your GCF!! Something else to note, if ALL of the terms in the polynomial have the SAME variable, then the GCF will have a variable as well. **

Two approaches you can take when factoring out a GCF from a polynomial are division and "filling in the blanks". Take a look at the examples and then choose the method that works best for you!

When factoring out a GCF given a polynomial expression, you first need to identify what the GCF is, and then divide each term in the polynomial by the GCF. Watch the videos below to learn how to factor a GCF using division. media type="youtube" key="fezUUGRw9JE" width="560" height="315"
 * Method 1: Dividing a Polynomial by the GCF**

In this approach you need to "undo" the distributive property. For this method, you still need to identify the GCF first, and then you can fill in the blanks with what is needed in order to get back to the original polynomial expression. Take a look at the examples below.
 * Method 2: Reversing the Distributive Property**

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 * Polynomials-Target C-Factoring GCF-Quick Check**

1) Factor the polynomial: -10x 5 + 14x 3 - 8x

2) Create a binomial that has a GCF of 5x.

3) Determine if 3x(4x 2 + 6x - 2) is the factored form of 12x 3 + 18x 2 - 6x.

Polynomials-Target C-Factoring GCF-Quick Check Solutions