Polynomial Question

[jashaan]

Hi there,
So i was wondering what polynomial topics/content is there in methods? I am trying to do a headstart and idk where to start for VCE polynomials. I have the basics such as remainder theorem, sketching basically, etc. For example this questions (i am struggling with):

the polynomial 2x^4 - x^3 - 5x^2 +3x can be factorised as x(2x-3)(ax^2 +bx +c). Find the values of a,b,c.

1. How do I factorise this polynomial?
2. Which VCE polynomials topic does this question fit in?

Thank you and good luck to all the year 12s with their exams <33

[fun_jirachi]

Hi there,
So i was wondering what polynomial topics/content is there in methods? I am trying to do a headstart and idk where to start for VCE polynomials. I have the basics such as remainder theorem, sketching basically, etc. For example this questions (i am struggling with):

the polynomial 2x^4 - x^3 - 5x^2 +3x can be factorised as x(2x-3)(ax^2 +bx +c). Find the values of a,b,c.

1. How do I factorise this polynomial?
2. Which VCE polynomials topic does this question fit in?

Thank you and good luck to all the year 12s with their exams <33

I can't comment on 2, since I don't do VCE, but I'd gladly help with 1, so here goes.


Other sites/textbooks will probably explain better than me, that's just a really really rough way of explaining it. If you want me to explain more, I can, feel free to ask! Hope I helped

[jashaan]

I can't comment on 2, since I don't do VCE, but I'd gladly help with 1, so here goes.


Other sites/textbooks will probably explain better than me, that's just a really really rough way of explaining it. If you want me to explain more, I can, feel free to ask! Hope I helped

hey there! Thank you heaps!! I really got an idea and it has helped me

[Bell9565]

Hey,
What year are you currently in? And are we talking about VCE units 1/2 or 3/4?
Pretty much it fits in the Functions and Graphs, where factorising polynomials is just a skill - but a very important skill!
Take a look at the study design on VCAA if you're not too sure what else you have to do.
Any questions let me know

[S_R_K]

Hi there,
So i was wondering what polynomial topics/content is there in methods? I am trying to do a headstart and idk where to start for VCE polynomials. I have the basics such as remainder theorem, sketching basically, etc. For example this questions (i am struggling with):

the polynomial 2x^4 - x^3 - 5x^2 +3x can be factorised as x(2x-3)(ax^2 +bx +c). Find the values of a,b,c.

1. How do I factorise this polynomial?
2. Which VCE polynomials topic does this question fit in?

Thank you and good luck to all the year 12s with their exams <33

An alternative to long division is equating coefficients.

For example, expanding out the factorised form, and writing coefficients in terms of a, b, c gives:



Then, since polynomials are identical if and only if their corresponding coefficients are equal, we have the following system of linear equations.



Clearly we have a = 1 and c = –1 (from the first and fourth equations), and then using either the second or third equation gives b = 1.

This method is worth studying because it tends to be more efficient - the leading coefficient and constant of a factor can usually be found by inspection (ie. in this example it's fairly obvious that a = 1 and c = -1), so you only need to set up and solve an equation to find the coefficient of a middle term.