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System Message

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

Houston (Customer)

[00:00:00] given a polynomial and one of its factors, find the remaining factors of the polynomial.
2x^3-5x^2-28x+15 ; x+3

Liz A (Tutor)

[00:00:07] Hi, how are you?

Houston (Customer)

[00:00:13] good you

Liz A (Tutor)

[00:00:39] I'm doing well, thanks! Do you have any ideas on how to start this problem?

Houston (Customer)

[00:00:55] I have already started onesec

Liz A (Tutor)

[00:03:01] That looks great!

Houston (Customer)

[00:03:06] idontknow what to do next

Liz A (Tutor)

[00:03:33] Now, we just need to see if we can factor 2x^2 - 11x + 5 anymore.

Houston (Customer)

[00:04:14] do I factor it the same? as ones without a number in front of x^2

Liz A (Tutor)

[00:04:49] How have you been factoring? By guess and check or using some method?

Houston (Customer)

[00:05:30] like 5x1=5 and 5+1=6 so that doesn't work

Liz A (Tutor)

[00:06:03] Ok. It sounds like you might be using something similar to the ac method. We can use a similar technique here but there are a couple of extra steps.

[00:06:41] Here, we still want to find two numbers that sum to the middle term, so we want to find two numbers that sum to -11.

[00:06:57] Does that sound familiar with the method you have been using to factor?

Houston (Customer)

[00:07:07] -11 and 1

Liz A (Tutor)

[00:07:55] Well, we also want those two numbers to multiply to 2 times 5. This is the part that is different. Since there is a number in front of x^2 we take that number and multiply it by the last numbers

Houston (Customer)

[00:08:31] no -10 and -1

Liz A (Tutor)

[00:08:41] Good. -10 and -1 will work.

[00:09:12] This part is also different. We take those two numbers and rewrite the middle term, -11x, as such. I'll write it on the white board.

Houston (Customer)

[00:10:22] would the answer be (x-10) and (x-1)

Liz A (Tutor)

[00:10:40] No, that is using the method when there is no number in front of the x^2 term.

[00:11:01] When there is a number in front of the x^2 term, we rewrite our middle term using the two numbers that we found and then factor.

[00:11:30] We have 2x^2 - 10x - 1x + 5. What we need to do, is split this into two and then factor each part seperately.

[00:12:17] I'm going to group the 2x^2 - 10x together and the -1x + 5 together. Now let's factor each of those separately. How can we factor 2x^2 - 10x?

Houston (Customer)

[00:12:38] idk

Liz A (Tutor)

[00:12:55] Do they have anything in common? For example a number and/or a variable

Houston (Customer)

[00:13:17] oh 2x

Liz A (Tutor)

[00:13:25] Good. Let's factor out a 2x.

[00:14:04] Great job!

[00:14:27] Perfect!

Houston (Customer)

[00:14:51] ok so is that the answer

Liz A (Tutor)

[00:14:53] When we combine all of the work we have done. We get that 2x^3 - 5x^2 - 28x + 15 = (x+3)(2x-1)(x-5)

[00:15:59] Do you have any questions about what we just went through?

Houston (Customer)

[00:16:06] nomam thanks

Liz A (Tutor)

[00:16:30] You're very welcome. Great work on this problem! Have a good night and I encourage you to fill out the survey at the end of the session.

Houston (Customer)

[00:16:39] ok bye