Question

I have an exam coming up tomorrow. Please help.
Find the degree of the the polynomial:
g(x) = (2x+1)(x-4)^3

Answer 1

I think the answer is 3 but I am not sure if I have to foil it.

Answer 2

no not 3

Answer 3

the degree of \((x-4)^3\) is 3, but you have another \(x\) term out front

Answer 4

yes, so there is an x^1 and degree of 3 so would I add it to 4?

Answer 5

@satellite73

Answer 6

Yeah, the degree of the polynomial is based off looking at it when it's in this form something like this, here this is just an arbitrary degree 5 polynomial.

\[f(x)=Ax^5+Bx^4+Cx^3+Dx^2+Ex+F\]

So basically what you need to do is multiply it out. Although along the way you might notice that there's a faster way to recognizing what it will eventually turn out to be without having the multiply it.

Answer 7

OK, so I would multiply it out to (x-4)(x-4)(x-4)(2x+1)... there is got to be a faster way to multiply that out or I would be taking a lot of time on the test

Answer 8

@Kainui

Answer 9

Yes, there is a faster way, but you'll discover it when you start multiplying it out. What do you think it'll turn out to be a degree of by just looking at it? Remember, the highest degree will be the term with all the x's in it.

Answer 10

I can see that the highest degree without multiplying it out is 3

Answer 11

Nope, sorry.

Answer 12

Actually, the coefficient 2x has a 1 so the highest should be 4

Answer 13

Wait, what do you mean?

Answer 14

The highest order term is 4, but I don't think how you go there was correct.

Answer 15

Let me see if I can try to explain what I mean

Answer 16

I see that there is a (2x+1) and a (x-4)^3 so the 2x has a degree of 1 and the x-4 has a degree of 3

Answer 17

That is where I came up with 4

Answer 18

I want to get there without having to multiply it all out

Answer 19

Yeah exactly, that's the correct explanation. Good. Yeah, the main thing is that I know you want to get the "quick" way but since you're not on the test it helps to do it the long way now. That way you understand where the quick method comes from, if that makes sense. Now is when you have the extra time to understand it so that on the test you can sort of do it more in your mind because you've been there and know what will happen.

Good luck on your test tomorrow!

Answer 20

Thanks! I understand doing it the long way to see the process. I just worry that I would make an error.