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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: kenhung123 on December 05, 2009, 12:26:01 am

Title: Factorised answer
Post by: kenhung123 on December 05, 2009, 12:26:01 am: Is there a need to factorise your final answer when not stated? Will there be a penalty?
E.g. 2x^2+4x+2
2(x^2+2x+1)
Title: Re: Factorised answer
Post by: Ilovemathsmeth on December 05, 2009, 12:31:40 am: Nah don't think you would lose marks. Though in differentiation with the product rule, I don't think they like very messy answers that can result often with powers and brackets - in such situations, I think it's better to be safe and just simplify as well as you can.
Title: Re: Factorised answer
Post by: TrueTears on December 05, 2009, 12:32:14 am: Sometimes factorising can lead to common factors which can be cancelled out.

So I'd look out for it but it is not a necessity.
Title: Re: Factorised answer
Post by: Ilovemathsmeth on December 05, 2009, 12:36:25 am: True, always look for common factors too - applicable to product rule and chain rule type questions usually.
Title: Re: Factorised answer
Post by: kenhung123 on December 05, 2009, 12:39:24 am: Hi can you expand on that? How does factorisation help in diff?
Title: Re: Factorised answer
Post by: TrueTears on December 05, 2009, 12:43:55 am: $y = 3\log_e(|x+3|) + \frac{x^2}{2} - x$

$\frac{dy}{dx} = \frac{2x^2+4x}{2x+6}$

$\frac{dy}{dx} = \frac{2(x^2+2x)}{2(x+3)}$

Cancel.
Title: Re: Factorised answer
Post by: Ilovemathsmeth on December 05, 2009, 12:58:42 am: Factorising helps when:

y = (x^2)(x + 3)^3

dy/dx = x^2 x 3 (x + 3)^2 + (x + 3)^3 x 2x

Taking (x + 3)^2 as a common factor.

(x + 3)^2 [3x^2 + 2x (x + 3)];

(x + 3)^2 [3x^2 + 2x^2 + 6x]

(x + 3)^2 [5x^2 + 6x]

x(x + 3)^2 [5x + 6]

It would be good to be familar with cancellation with something like:

x(5x + 6) divided by x(5x + 6)^2 as you can cancel the x and then cancel the (5 x + 6) in the numerator giving 1/(5x + 6)
Title: Re: Factorised answer
Post by: kenhung123 on December 05, 2009, 01:12:51 am: Thank you for help!
Title: Re: Factorised answer
Post by: Ilovemathsmeth on December 05, 2009, 01:14:34 am: I'm hopelessly in love with Maths, it's always exciting to help out provided it's not CAS, I'm not fully competent with that course. I'm hoping Matrices knowledge from Further will help me get through.