# Unit 4- Factoring Polynomials

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#1
How do you factor: 2x^2n + 7x^n – 15 ?

I'm confused because I've never worked it out when the equation has powers (^2n...) :/

Thanks!!!
0
4 years ago
#2
Hey Rosa

You know how you factorise 2x2 + 7x - 15? You can literally do the same thing, and at the end just replace your xs with xns
2
#3
(Original post by Student403)
Hey Rosa

You know how you factorise 2x2 + 7x - 15? You can literally do the same thing, and at the end just replace your xs with xns
Okay, I've got it Pretty simple, now that I understand
Thank you!
0
4 years ago
#4
(Original post by RosaA)
Okay, I've got it Pretty simple, now that I understand
Thank you!
My pleasure and thanks for the tag

I hope you understand the reason why btw!
Spoiler:
Show
Because 2x2n = 2(xn)2 and so on

You could do the same with a quadratic involving anything like that instead of an x.. Even a function like 2cos2θ +7cosθ - 15
0
4 years ago
#5
(Original post by RosaA)
How do you factor: 2x^2n + 7x^n – 15 ?

I'm confused because I've never worked it out when the equation has powers (^2n...) :/

Thanks!!!
In addition to 403's excellent answer: This is called a disguised quadratic (in this case, it's a quadratic in ). What this fancy shmoozy wording means is that if you make a substitution (I always make this explicit substitution when working out problems like this) then you have a quadratic in or a quadratic in written as .

I'd make the substitution, re-write everything in terms of and then do my cool quadratic work with awesome quadratic skillz and then convert everything back to by back-substitution .
1
4 years ago
#6
Oh, and moved to maths.
0
4 years ago
#7
(Original post by RosaA)
How do you factor: 2x^2n + 7x^n – 15 ?

I'm confused because I've never worked it out when the equation has powers (^2n...) :/

Thanks!!!
I'll show you an example - suppose the case where n = 2, and we have the equation .

Now, we can factorise this the regular way (i.e. the way we do quadratic equations as 403 mentioned)

Now, it seems that we have two equations from which we can obtain factors:

We can now evaluate these two equations to obtain our roots, so with the first one,

, as taking a square root gives us two solutions.

However, for the second equation, note that it leads to and at GCSE level, you can't take the square root of negative numbers so we have to eliminate this solution .

We only have two solutions in this case:

I hope this example helped!
2
4 years ago
#8
(Original post by Zacken)
In addition to 403's excellent answer: This is called a disguised quadratic (in this case, it's a quadratic in ). What this fancy shmoozy wording means is that if you make a substitution (I always make this explicit substitution when working out problems like this) then you have a quadratic in or a quadratic in written as .

I'd make the substitution, re-write everything in terms of and then do my cool quadratic work with awesome quadratic skillz and then convert everything back to by back-substitution .
PRSOM
0
#9
(Original post by aymanzayedmannan)
I'll show you an example - suppose the case where n = 2, and we have the equation .

Now, we can factorise this the regular way (i.e. the way we do quadratic equations as 403 mentioned)

Now, it seems that we have two equations from which we can obtain factors:

We can now evaluate these two equations to obtain our roots, so with the first one,

, as taking a square root gives us two solutions.

However, for the second equation, note that it leads to and at GCSE level, you can't take the square root of negative numbers so we have to eliminate this solution .

We only have two solutions in this case:

I hope this example helped!
Yes, it was very helpful indeed!! Thank you so much !!
1
#10
(Original post by Zacken)
In addition to 403's excellent answer: This is called a disguised quadratic (in this case, it's a quadratic in ). What this fancy shmoozy wording means is that if you make a substitution (I always make this explicit substitution when working out problems like this) then you have a quadratic in or a quadratic in written as .

I'd make the substitution, re-write everything in terms of and then do my cool quadratic work with awesome quadratic skillz and then convert everything back to by back-substitution .
I need your brain -literally Thanks so much!!
0
#11
(Original post by Student403)
My pleasure and thanks for the tag

I hope you understand the reason why btw!
Spoiler:
Show
Because 2x2n = 2(xn)2 and so on

You could do the same with a quadratic involving anything like that instead of an x.. Even a function like 2cos2θ +7cosθ - 15
No it's cool, no need to thank me -I owe you .

Yup, I understand it now
1
4 years ago
#12
(Original post by RosaA)
No it's cool, no need to thank me -I owe you .

Yup, I understand it now
Love it when people say that
0
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