ACT Math : How to factor a common factor out of squares

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Factoring Squares

Which real number satisfies ?

 

Possible Answers:

Correct answer:

Explanation:

Simplify the base of 9 and 27 in order to have a common base.

(3x)(9)=272

= (3x)(32)=(33)2

=(3x+2)=36

Therefore:

x+2=6

x=4

 

 

Example Question #122 : Exponents

Which of the following is a factor of  ?

Possible Answers:

Correct answer:

Explanation:

The terms of  have  as their greatest common factor, so

 is a prime polynomial. 

Of the five choices, only  is a factor.

Example Question #1 : How To Factor A Common Factor Out Of Squares

Simplify  

Possible Answers:

Correct answer:

Explanation:

The easiest way to approach this problem is to break everything into exponents.  is equal to  and 27 is equal to . Therefore, the expression can be broken down into . When you cancel out all the terms, you get , which equals .

Example Question #4 : Factoring Squares

Which of the following expression is equal to

 

Possible Answers:

Correct answer:

Explanation:

When simplifying a square root, consider the factors of each of its component parts:

Combine like terms:

Remove the common factor, :

Pull the  outside of the equation as :

                       

Example Question #2 : How To Factor A Common Factor Out Of Squares

Which of the following is equal to the following expression?

Possible Answers:

Correct answer:

Explanation:

First, break down the components of the square root:

Combine like terms. Remember, when multiplying exponents, add them together:

Factor out the common factor of :

Factor the :

Combine the factored  with the :

Now, you can pull  out from underneath the square root sign as :

Example Question #4 : Squaring / Square Roots / Radicals

Which of the following expressions is equal to the following expression?

Possible Answers:

Correct answer:

Explanation:

First, break down the component parts of the square root:

Combine like terms in a way that will let you pull some of them out from underneath the square root symbol:

Pull out the terms with even exponents and simplify:

Example Question #4 : How To Factor A Common Factor Out Of Squares

What is,

 ?

Possible Answers:

Correct answer:

Explanation:

To find an equivalency we must rationalize the denominator.

To rationalize the denominator multiply the numerator and denominator by the denominator.

 

Factor out 6,

 

Extract perfect square 9 from the square root of 18.

 

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