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If you factor by the greatest common factor, you can be assured that there are no common factors left. That is not the case if factoring is by an ordinary common factor.

For example,

3 is a common factor of 30 and 36. 30/36 = 10/12.

But 10 and 12 have a common factor: 2.

6 is the GCF of 30 and 36 and 30/36 = 5/6. 5 and 6 have no common factor (other than 1).

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โˆ™ 2014-05-31 12:12:32
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Algebra

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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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โˆ™ 2010-11-18 17:55:45

When you divide 2 or more numbers by a common factor which is not the greatest common factor, they will still have a common factor which is greater than 1. When you divide them by their greatest common factor, the quotients are coprime - that is, they no longer have a factor in common other than 1.

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โˆ™ 2017-03-20 12:17:01

Factoring with a common factor will not get you the simplest form, factoring with the GCF will.

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Q: What is different about factoring with a common factor and factoring by the greatest common factor?
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Related questions

What is the first thing you do when factoring an expression?

Factor out the Greatest Common Factor.


What are the kinds of factor?

factoring whole numbers,factoring out the greatest common factor,factoring trinomials,factoring the difference of two squares,factoring the sum or difference of two cubes,factoring by grouping.


What is the greatest common factor of 7e and 7e2?

Additive factoring.7e + 7e2= 7e(1 + e)----------------------so,7e=====greatest common factor


When factoring a trinomial why can't one of the monomials have a greatest common factor?

What makes a greatest common factor "common" is comparing at least two terms and finding something common between them.


Factor by factoring out the greatest common factor -7x5y3-42x3y2 plus 35xy?

-7xy(x4y2 + 6x2y - 5)


What is the meaning of GCF of monomial?

gcf is Greatest Common Factor. It means what is the largest value that can go into what you are factoring.


How do you solve a factoring polynomials problem if there is no greatest common factor?

If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised.


What is the greatest factor of 25 and 70?

The greatest common factor? Start by factoring both numbers into primes: 25 = 5*5 70 = 2*5*7 The only prime factor in common is a single 5. So the answer is 5.


In factoring a trinomial with a leading coefficient other than 1 what is the first step?

find a greatest common factor or GCFin factoring a trinomial with a leading coefficient other than 1 the first step is to look for a COMMON factor in each term


Why do you need to learn factoring in Algebra?

You need to learn it, so you can learn Greatest Common Factor, which you need to reduce fractions.


How do you find the greatest common factor for fifteen and twentyfive?

Factoring: 25 = 5x5 and 15 = 5x3. So the factors of 25 and 5 and 5, and the factors of 15 are 3 and 5. The greatest common factor therefore is 5.


Can one be a GCF?

One can be a greatest common factor. Though it does not happen often, there are numbers that the only number that they share when factoring is one. An example of this is the numbers two and three. The greatest common factor of two and three is one.

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