Find the greatest typical factor of 2 or much more expressionsFactor the greatest typical factor indigenous a polynomialFactor by grouping

Find the Greatest typical Factor of 2 or more Expressions

Earlier we multiplied components together to acquire a product. Now, we will be reversing this process; we will begin with a product and then break it down right into its factors. Splitting a product into components is referred to as factoring.

You are watching: How to find gcf with variables and exponents

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Find the GCF that 48 and also 80.


16


Find the GCF of 18 and 40.


2


We summary the measures we usage to uncover the GCF below.


Find the Greatest common Factor (GCF) of 2 expressions.
Factor each coefficient into primes. Compose all variables through exponents in broadened form.List all factors—matching common factors in a column. In each column, one the common factors.Bring under the usual factors the all expressions share.Multiply the factors.

In the first example, the GCF was a constant. In the next two examples, we will acquire variables in the greatest usual factor.


Find the greatest usual factor of

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Multiply the factors.
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and also
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Multiply the factors.
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and also
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Multiply the factors.
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,
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.


Solution
Find the GCF the 5a and 5.
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Rewrite every term as a product making use of the GCF.
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Check by mulitplying the determinants to gain the orginal polynomial.
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Rewrite each term together a product using the GCF.
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Check by mulitplying the factors.
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Rewrite every term as a product making use of the GCF.
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Check by mulitplying.
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Rewrite every term.
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Check.
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Factor the GCF.
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Rewrite every term.
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Check.
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Check.
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Rewrite each term using the GCF.
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Check.
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Check on your very own by multiplying.

Factor:

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Factor:

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Factor by Grouping

When there is no usual factor of every the regards to a polynomial, look because that a typical factor in simply some the the terms. When there are four terms, a good way to begin is by separating the polynomial into two parts with two terms in every part. Climate look because that the GCF in each part. If the polynomial can be factored, girlfriend will uncover a typical factor increase from both parts.

(Not all polynomials can be factored. Just like some numbers room prime, part polynomials room prime.)


How to factor by Grouping

Factor:

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Solution
Factor:
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Factor:

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Factor by grouping.
Group terms with usual factors.Factor the end the common factor in each group.Factor the typical factor indigenous the expression.Check by multiply the factors.

Factor:

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Solution

Factor:

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Factor:

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Access these online sources for extr instruction and also practice v greatest usual factors (GFCs) and also factoring by grouping.


Key Concepts

Finding the Greatest common Factor (GCF): To discover the GCF of 2 expressions:Factor every coefficient into primes. Create all variables through exponents in broadened form.List every factors—matching common factors in a column. In each column, one the usual factors.Bring down the typical factors that all expression share.Factor the Greatest typical Factor from a Polynomial: To aspect a greatest typical factor indigenous a polynomial:Find the GCF of all the terms of the polynomial.Rewrite each term together a product using the GCF.Use the ‘reverse’ Distributive property to factor the expression.Factor through Grouping: To aspect a polynomial with 4 4 or more termsGroup terms with usual factors.Factor out the typical factor in each group.Factor the usual factor indigenous the expression.
Practice provides Perfect

Find the Greatest usual Factor of two or much more Expressions

In the adhering to exercises, discover the greatest typical factor.


8, 18


2


24, 40


72, 162


18


150, 275


10a, 50


10


5b, 30


Factor the Greatest typical Factor native a Polynomial

In the following exercises, element the greatest common factor from every polynomial.


Factor by Grouping

In the adhering to exercises, variable by grouping.


Mixed Practice

In the following exercises, factor.


Everyday Math

Area the a rectangle The area the a rectangle with length 6 much less than the broad is provided by the expression

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, where
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width. Variable the greatest usual factor from the polynomial.


Height the a baseball The elevation of a baseball t seconds after the is hit is given by the expression

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. Variable the greatest typical factor indigenous the polynomial.


Writing Exercises

The greatest typical factor of 36 and also 60 is 12. Define what this means.


Answers will vary.


What is the GCF the

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? create a general dominion that tells you just how to discover the GCF the
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Self Check

ⓐ After completing the exercises, usage this checklist to evaluate your mastery the the goals of this section.

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ⓑ If many of your checks were:

…confidently. Congratulations! you have completed your objectives in this section! Reflect on the study skills you supplied so that you can proceed to use them. What go you carry out to end up being confident of your capability to execute these things? be specific!

…with part help. This have to be addressed conveniently as subject you carry out not master come to be potholes in your road to success. Math is sequential—every topic builds upon previous work. It is important to make sure you have a strong structure before you relocate on. Who have the right to you ask because that help? Your other classmates and instructor are good resources. Is over there a ar on campus wherein math tutors room available? deserve to your study skills be improved?

…no – i don’t gain it! This is an essential and you should not neglect it. You must get aid immediately or friend will easily be overwhelmed. Watch your instructor as quickly as possible to talk about your situation. With each other you can come up with a setup to acquire you the help you need.

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Glossary

factoringFactoring is dividing a product right into factors; in other words, that is the reverse procedure of multiplying.greatest common factorThe greatest typical factor is the biggest expression that is a variable of two or more expressions is the greatest usual factor (GCF).
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