How do you find greatest common factor from a polynomial?

Answer 1

Look at the numbers (coefficients) in the problem. Use your knowledge of multiplication / division to think of the largest common factor of these coefficients, in other words, the largest number that divides into all of them.

Assuming one variable is common to all the individual terms, find the smallest exponent. That will be the variable part of the GCF.

Alternate method. This is probable what your book and teacher will tell you to do when you are first learning to do this.

Do a prime factorization of each term. Look for common factors in EVERY term. All these common factors become part of the GCF and are moved to the front of the parenthesis. All other factors are left inside the parenthesis. Simplify both outside and inside the parenthesis by multiplying and using exponents for variables.

Ex: 30 x5y2 + 45x3y4

= 2 . 3 . 5 . x . x . x . x . x . y . y + 3 . 3 . 5 . x . x . x . y . y . y . y

look for common factors 3,5,x,x,x,y,y <-- these go outside the parenthesis. the "left overs" go inside the parenthesis.

= (3 . 5 . x . x . x . y . y )(2 . x . x + 3 . y . y )

= 15 x3y2 ( 2 x2 + 3 y2) <-- this is the answer.

Notice that the original problem had 2 terms and now there are 2 terms inside the parenthesis.

Answer 2

First.. find the gcf of the coefficients.

Second.. remember the word 'common' .. for the variables only variables that appear in all the monomials are common factors, look at the exponents of that common variable, use the smallest exponent for that variable.

Third.. Put them all together.. that is the gcf.

EX: Find the gcf for 15x2y6 and 12x3yz

The gcf of the coefficients, 15 and 12, is 3.

x is a common variable ... its smallest exponent is 2 .... x2

y is a common variable ... its smallest exponent is an understood 1 ... y

note that z is NOT a common variable

So the GCF is 3x2y

Answer 3

since it is a single term it cannot have a common factor.

If you give a specific example of what you are looking for we would be glad to help!

Answer 4

You need at least two terms to find a GCF.

Answer 5

The largest value by which all of its terms are divisible.

Answer 6

You need at least two terms to find a GCF.