ACT Math : Factoring Equations

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #211 : Equations / Inequalities

A certain number squared, plus four times itself is equal to zero. 

Which of the following could be that number?

Possible Answers:

Correct answer:

Explanation:

The sentence should first be translated into an equation. 

We will call the "certain number" .

This gives us .

So solve this we can factor out an  to get .

This makes the zeros of the equation evident. We know that when  the entire expression will equal zero, making the equation true. We also know that when , the quantity  will be , which also satisfies the equation.

Therefore, the two possible solutions are  and .

Example Question #212 : Equations / Inequalities

If , and , which of the following is a possible value of ?

Possible Answers:

-6

-4

-8

-2

-12

Correct answer:

-12

Explanation:

The given expression is a quadratic equation; therefore, we can factor the equation 

Use the format of the standard quadratic equation:

Since , we know that the quadratic's roots will resemble the following:

We also know that one of those signs has to be negative, since our two last terms multiply to equal the variable , and  is negative in our quadratic. Now, we need to find two numbers that when multiplied together equal -24, and equal 10 when they are added together. Let's start by finding the factors of 24. The factors of 24 are 24 and 1, 12 and 2, 8 and 3, 6 and 4. Since one of those factors will be negative in our factored equation, we need to find the two factors whose difference is 10.

This means that the numbers in the factored equation are 12 and -2; thus, we may write the following:

.

By the zero multiplication rule, either portion of that equation can equal 0 for the result to be 0; thus, we have the following two expressions:

 

Subtract 12 from both sides of the equation:

Calculate the value of the variable in the second equation.

Add 2 to both sides of the equation.

Since we want a negative answer for our variable, the correct answer is:

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