SOLUTION: Hi, I have a quadratic factorization question that I don't know how to do... It's a Year 11 Maths question: 4x^4-37x^2+9 I have to factorize that and I would show you wh

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Question 263772: Hi,
I have a quadratic factorization question that I don't know how to do...
It's a Year 11 Maths question:
4x^4-37x^2+9
I have to factorize that and I would show you what I've done so far but I have no idea how to do this question...
Thank you so much for your help! :)
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) (Show Source):
You can put this solution on YOUR website!
Hi,
I have a quadratic factorization question that I don't know how to do...
It's a Year 11 Maths question:
4x^4-37x^2+9
I have to factorize that and I would show you what I've done so far but I have no idea how to do this question...
Thank you so much for your help
4x^2-37x^2+9=0
4x^4-36^2 -x^2+9=0
4x^2(x^2-9)-1(x^2-9)=0
(4x^2-1)(x^2-9)=0
(2x+1)(2x-1)(x+3)(x-3)=0

Answer by ikleyn(53712) (Show Source):
You can put this solution on YOUR website!
.
Hi,
I have a quadratic factorization question that I don't know how to do...
It's a Year 11 Maths question:
4x^4-37x^2+9
I have to factorize that and I would show you what I've done so far but I have no idea how to do this question...
Thank you so much for your help
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Factorize your polynomial step by step

4x^2 - 37x^2 + 9 =
= 4x^4 - 36^2*x^2 - x^2 + 9
= 4x^2(x^2-9) - (x^2-9)
= (4x^2-1)*(x^2-9)
= (2x+1)(2x-1)(x+3)(x-3)

The difference between my solution and the @mananth solution is that
@mananth makes his transformations on an equation (which is not needed),
while I make transformations over the polynomial, exactly as it is requested.