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Maths question- A level help please

Hey,

The question asks g(x)=x^9-7x^6-8x^3 and to write this in the form x^3(x^3+a)(x^3+b)
where a and b are integers.

I tried to use the method where u=x^n however in the mark scheme it doesn't match what I've got.

I tried to divide g(x) by x^3 and got x^3-7x^2-8 as I thought that the rule was that when there's a bracket between the indices it's multiplied.
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mqb2766
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Original post by Voss.gloss20
Hey,

The question asks g(x)=x^9-7x^6-8x^3 and to write this in the form x^3(x^3+a)(x^3+b)
where a and b are integers.

I tried to use the method where u=x^n however in the mark scheme it doesn't match what I've got.

I tried to divide g(x) by x^3 and got x^3-7x^2-8 as I thought that the rule was that when there's a bracket between the indices it's multiplied.

g(x) = x^3(x^6 - 7x^3 - 8)
Not sure what you were doing? Then it's a hidden quadratic.
First, consider the two expressions side by side:

g(x)=x9−7x6−8x3g(x)=x^{9}-7x^{6}-8x^{3}

g(x)=x3(x3+a)(x3+b)g(x)=x^{3}(x^{3}+a)(x^{3}+b)

As already suggested, you should be able to see that you can initially factorise the first expression by simply taking out the x3x^{3} and rewriting as:
g(x)=x3(x6−7x3−8)g(x)=x^{3}(x^{6}-7x^{3}-8)

So now you need to factorise (x6−7x3−8)(x^{6}-7x^{3}-8) in the form (x3+a)(x3+b)(x^{3}+a)(x^{3}+b)

(For anyone who struggles with factorising, you can say that x3=px^{3}=p, then factorise p2−7p−8p^{2}-7p-8, then sub x3x^{3} back in).
Just expand the RHS and compare coefficients to find a and b then plug those into the factorise form nice and easy
Original post by Voss.gloss20
I tried to divide g(x) by x^3 and got x^3-7x^2-8 as I thought that the rule was that when there's a bracket between the indices it's multiplied.


xaxb=xa−b\dfrac{x^a}{x^b}=x^{a-b} rather than xabx^{\frac{a}{b}}

That was your misconception.
Thanks all :smile: I understand what I was doing wrong now.

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