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1.1 Greatest Common Factor: Vocabulary

 

Factor: A factor is a number, variable or quantity that is being multiplied.

 

Two factors:

 

Three factors:

 

Two factors:

2 (x+1)

Two factors:

(x-3)(x2 + 2x + 1)

 

Factoring, To Factor a Quantity, To Rewrite a Quantity as a Product

To rewrite a quantity as factors or to rewrite a quantity as something times something else:

 

The factored form of  

The factored form of  

The factored form of  

 

Remember, the operation of multiplication holds factors together.

 

Greatest Common Factor (GCF)

The largest integer, variable or quantity factor that is a factor of all of the given terms.

 

;GCF = 2

;GCF = x

; GCF = x+1

 

Integers

The counting numbers {1, 2, 3, 4, …}, their negatives, and zero.  Mathematicians use the letter  to indicate the set of integers.  

 

 

Polynomial

A sum or difference of terms, where the exponents are positive integers or 0 and the coefficients are real numbers.  The word polynomial comes from Greek words (“polus”  and “nomos” ) meaning “many parts.”

 

A polynomial with 4 terms:

 

A polynomial with 2 terms:

 

Not a polynomial:

 

(why?)

 

 

 

 

Product

The result obtained from multiplying factors together or the answer to a multiplication problem.

 

6 is the product

 

2x+2 is the product:

 

 

 

To “find the product” means to find the result of multiplying factors together.

To “rewrite something as a product” to rewrite the quantity as a multiplication problem or as factors.

 

Write 20 as a product:  

Write 2x + 4 as a product:2(x+2)

 

 

Term: A single number, a single variable or a group of factors. Terms are separated by plus signs, minus signs or equal signs.

 

1 term:

5

1 term:

 

2 terms:

3(x+1) + x(x+1)

 

1 term:

a

 

4 terms:

 

 

 

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