**Session Date:**7/27/2015 11:21AM ET

**Length:**44.8 minute(s)

**Subject:**Live Math Tutoring - MTH/209

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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

TERRI (Customer)

[00:00:00] Can someone help me understand how to factor a trinomial?

[00:00:06] Hi Steve

Steve H (Tutor)

[00:00:19] Hello Terri.
How are you today?

TERRI (Customer)

[00:00:26] I'm doing okay.

[00:00:28] thank you.

[00:00:29] you?

Steve H (Tutor)

[00:00:48] I doing well.
What kind of problem are you working on today?

TERRI (Customer)

[00:01:03] Okay, I'll write it up on the board.

Steve H (Tutor)

[00:01:13] Sounds good.

TERRI (Customer)

[00:02:24] I have to factor the trinomial completely or find out if it's the trinomial prime.

[00:02:33] I don't understand how to do either.

[00:02:52] I've read the examples and videos and still do not understand it

Steve H (Tutor)

[00:03:06] OK. The trinomial is prime if we can't factor it.
So, if we can factor it, then it is not prime.

TERRI (Customer)

[00:03:16] ok

[00:03:21] i understand that

Steve H (Tutor)

[00:03:27] Factoring is the opposite of FOIL.
Are you familiar with FOIL?

TERRI (Customer)

[00:03:40] I didn't get a chance to read up on foil

[00:03:46] I've seen it

Steve H (Tutor)

[00:04:06] So, on the white board I will show you a FOIL problem.

TERRI (Customer)

[00:04:11] ok

Steve H (Tutor)

[00:05:00] FOIL stands for first, outside, inside, last.
We multiply those four pairs of numbers to get this problem simplified.

TERRI (Customer)

[00:06:35] ok

[00:06:39] I see how you did that

Steve H (Tutor)

[00:06:44] The two middle terms combined to get 11x.

TERRI (Customer)

[00:06:51] right

Steve H (Tutor)

[00:07:18] Good.
Now factoring is going in the opposite direction.
We have to figure out what two binomials will multiply to make the original trinomial.

[00:07:40] The first thing I would do with your problem is write it in the order with the highest power first.

TERRI (Customer)

[00:08:02] Oh okay, so I can rewrite it

Steve H (Tutor)

[00:08:37] Yes, you can write it in any order you want, just be sure that the signs on the numbers stay on them.
Notice the 9x is still negative.

TERRI (Customer)

[00:08:47] yes

Steve H (Tutor)

[00:09:11] Now we have to figure out what two binomials will multiply to this trinomial if I FOIL them out.

[00:10:24] So, you have to use the numbers in the problem to give you some clues.
For example, the first term is 4x^2.
What are two things that can be multiplied to make 4x^2?

TERRI (Customer)

[00:11:41] 2(2) and 2(1)

Steve H (Tutor)

[00:12:07] You are correct about 2 and 2, but I think you mean 4 and 1.
Correct?

TERRI (Customer)

[00:12:47] I was thinking 2x2=4 and 2x1=2

Steve H (Tutor)

[00:13:22] The two numbers have to multiply to 4, so the only options are 2(2) or 4(1).

TERRI (Customer)

[00:13:30] oh okay

[00:13:48] so now I have to find two things for 2?

Steve H (Tutor)

[00:14:23] Here is where you can play around with the options and try to figure them out or you can use a method that will work them out every time.
Would you like me to show you that method?

TERRI (Customer)

[00:14:37] Yes please.

[00:14:42] Thank you.

Steve H (Tutor)

[00:15:22] Let's use a different example for now.
I will show you on the white board.

TERRI (Customer)

[00:15:27] ok

Steve H (Tutor)

[00:16:01] Step 1 - Multiply the first number and the last number (once it is written in this order).

TERRI (Customer)

[00:16:32] ok

Steve H (Tutor)

[00:16:49] Step 2 - Figure out the two numbers that multiply to that answer (-10) and add up to the middle number (9).

[00:17:30] The two numbers are 10 and -1 because 10(-1) is -10 and 10+(-1) is 9.
Does this make sense?

TERRI (Customer)

[00:17:51] yes

Steve H (Tutor)

[00:18:18] Step 3 - Rewrite the problem with the middle term replaced by the two terms that add to it.

TERRI (Customer)

[00:18:58] ok

Steve H (Tutor)

[00:19:02] Notice that I am breaking apart the 9x into two pieces that if combined would equal 9x.

TERRI (Customer)

[00:19:14] I see that

Steve H (Tutor)

[00:19:32] Step 4 - put parenthesis around the first two terms and the last two terms.

TERRI (Customer)

[00:20:02] ok

Steve H (Tutor)

[00:20:17] Notice that I included the sign with the 1x.
That is very important.

TERRI (Customer)

[00:20:41] ok

Steve H (Tutor)

[00:20:59] Step 5 - factor out any GCF within each parenthesis.

[00:21:26] Notice that in the first parenthesis, both are divisible by 2.
In the second parenthesis both are divisible by -1.

[00:21:42] I meant 2x in the first parenthesis.

TERRI (Customer)

[00:21:46] I see

Steve H (Tutor)

[00:22:49] Here is where you will know if you are correct.
If the parenthesis match, then you know you have it correct.
The answer is written on the white board.

TERRI (Customer)

[00:23:26] I don't understand the last part

[00:23:45] you have (x+5) and (2x-1)

Steve H (Tutor)

[00:24:17] OK.
When you have matching parenthesis, you write that down as the first factor and the remaining outside factors get put into the second parenthesis.

TERRI (Customer)

[00:24:34] oh okay

[00:24:35] I see

Steve H (Tutor)

[00:24:48] Do you want to try this process with your problem?

TERRI (Customer)

[00:25:06] ok

Steve H (Tutor)

[00:25:18] What would the first step be?

TERRI (Customer)

[00:25:35] multiply the first and at number?

Steve H (Tutor)

[00:25:45] Yes.
What would you get?

TERRI (Customer)

[00:26:00] I would get 20

Steve H (Tutor)

[00:26:12] Correct.
What is the next step?

TERRI (Customer)

[00:27:02] the next step is to figure out the two numbers that multiply to that answer (20) and add that adds up to the middle number -9

Steve H (Tutor)

[00:27:23] That is absolutely correct.
What would those two numbers be?

TERRI (Customer)

[00:27:34] 4 and 5

Steve H (Tutor)

[00:28:06] You are definitely thinking correctly.
However, 4+5 is 9.
We need them to add to -9.
How could we adjust this?

TERRI (Customer)

[00:28:47] -4 and 5

Steve H (Tutor)

[00:29:02] Remember that if you multiply two negative numbers together, the answer is positive.
But if you add two negative numbers together, you will get a bigger negative number.

TERRI (Customer)

[00:29:26] -4-5 = -9

Steve H (Tutor)

[00:29:46] That is correct.
Both numbers need to be negative.
So, -4 and -5 is correct.

TERRI (Customer)

[00:29:56] ok

Steve H (Tutor)

[00:30:03] What is the next step?

TERRI (Customer)

[00:30:29] The next step is to rewrite the problem with the middle term replaced by the two terms that add to it.

[00:30:33] -4 and -5

Steve H (Tutor)

[00:30:42] Excellent!

[00:31:11] And now we do . . .?

TERRI (Customer)

[00:31:22] add the parentheses

Steve H (Tutor)

[00:31:56] Correct.
Now what do you think the factors would be out of the first parenthesis and the second parenthesis?

TERRI (Customer)

[00:33:38] It would be 4x(x+5)
for the first one?

[00:33:58] I mean4x(x-5)

Steve H (Tutor)

[00:34:40] The factor of 4x is correct, but it would be 4x(x-1) because 4x times -1 would be -4x.

[00:35:03] How about the second one?

TERRI (Customer)

[00:35:13] oh okay so that would be the same for the 2nd one correct?

Steve H (Tutor)

[00:36:06] Notice that both have a 5 in them, so you could factor out a 5.
However, since the first term is negative, you actually want to factor out a -5.
This would give you -5(x-1).

[00:36:26] Notice that if you distribute you will get back to where you started.

TERRI (Customer)

[00:36:40] I see

Steve H (Tutor)

[00:36:51] Notice now that both parenthesis are the same.

TERRI (Customer)

[00:36:57] yes

Steve H (Tutor)

[00:37:09] So, we are ready to write the answer.
What do you think?

TERRI (Customer)

[00:39:13] Looking at how you did the example that you provided before this one.
I am going to take a guess: (x-1) (2x-1)

[00:39:39] I got it wrong?

Steve H (Tutor)

[00:40:09] Not quite, though you do have the first term correct.
Notice both parenthesis are (x-1).
What is outside each parenthesis?

TERRI (Customer)

[00:40:29] 4x-5

Steve H (Tutor)

[00:40:55] There you go.
So, the second parenthesis would be (4x-5).

TERRI (Customer)

[00:41:12] ok

[00:41:27] my goodness.

[00:41:48] I thought I knew what you were talking about in the last example.
I now know...

Steve H (Tutor)

[00:41:59] Yes.
It is a process, but a process that works every time.

TERRI (Customer)

[00:42:05] ok

[00:42:15] Thanks Steve

Steve H (Tutor)

[00:42:30] Do you want me to make up another example?

TERRI (Customer)

[00:42:52] no, let me try some on my own.
I'm sure I'll be back.

[00:43:01] Thanks for helping understand the process.

Steve H (Tutor)

[00:43:06] Ok.
Good luck.
We are always here.

TERRI (Customer)

[00:43:06] I greatly appreciate it

Steve H (Tutor)

[00:44:26] Have a good afternoon.

TERRI (Customer)

[00:44:37] Thank you.
You as well.