GCF and Factoring Polynomials

GCF and Factoring Polynomials

By Ms. Costa

• ​Guess and check

• Use a factor tree and multiply the common prime numbers​

​Two Methods:

• stands for "Greatest Common Factor"​

• when you have a set of numbers, the GCF is the largest positive integer that divides evenly into all the numbers​ (or variables)

GCF

First find the GCF

Multiple Choice

What is the Greatest Common Factor of 18 and 54?

• 9

• 6

• 54

• 18

• 3

We multiplied polynomials using distributive property.

Now we can work backward and pull a monomial factor out of a polynomial​

​

Use the distributive property​

​1.6w² + 6w

Step One: Find the GCF of each term

​

​Step Two: Write each term as a product of the GCF and remaining factors.

​

Step Three: Distributive Property​​

27y² + 18y​

Step One: Find the GCF of each term

​

​Step Two: Write each term as a product of the GCF and remaining factors.

​

Step Three: Distributive Property​​

-4a²b-8ab²+2ab​

Multiple Choice

15w - 3v

• 5(3w - 3v)

• 3w(5 - 3v)

• 3(5w - v)

• 3v(5w)

Multiple Choice

7u²t² + 21ut² - ut

• 7(u²t² + 3ut² - ut)

• ut(7ut + 21t - 1)

• u(7ut² + 21t² - t)

• t(7u²t + 21ut - u)

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Multiple Choice

Factor: 3x² + 4x

• x(3x + 4)

• 3x(x + 4x)

• 3(x² +4x)

• x²(3+4)

Multiple Choice

Can this binomial be factored?

4x² + 7

• Yes

• No

Multiple Choice

Can this binomial be factored?

5x - 4

• Yes

• No

Multiple Choice

Can this binomial be factored?

x² + 3x

• Yes

• No