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Factor the trinomial completely.


Select the correct choice below

(a) x^2+24x+13=?

(b) The polynomial is prime.

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1 Answer

In order to understand how to factor x^2 + 24x + 13, it is helpful to understand how to F-O-I-L. F-O-I-L stands for First, Outer, Inner, Last. When you try to factor out x^2 + 24x + 13 into (       )(      ), you want to think about what you would get if you F-O-I-L your answer, because when you F-O-I-L your answer, you should get the original equation, x^2 + 24x + 13.

1) You know you want the First two (the F in F-O-I-L) to multiply to make x^2, therefore you know you will start out with

(x      )(x      )

2) Then, you know you want the Last two (the L in F-O-I-L) to multiply to make 13, and the only two numbers that multiply to make 13 are 1 and 13

(x + 13)(x + 1)

3) Now let's F-O-I-L our answer to check to see if we get the original equation. This will tell us if we factored properly.

First: x times x = x^2

Outer: x times 1 = 1x

Inner: 13 times x = 13x

Last: 13 times 1 = 13

Now add all of them together: x^2 + 1x + 13x + 13 = x^2 + 14x + 13.

We did not get our original equation, x^2 + 24x + 13, and since there are no other numbers to choose that multiply to make 13, this equation is not factorable. Therefore, the answer is b.

An example of an equation that is factorable would be x^2 + 2x + 1

It would be equal to (x + 1)(x + 1)

First: x times x = x^2

Outer: x times 1: 1x

Inner: 1 times x = 1x

Last: 1 times 1 = 1

Add all four together: x^2 + 1x + 1x + 1 = x^2 + 2x + 1

Hope this helps! Let me know if you have any other questions! :)