VCE Methods Question Thread!

[Bluegirl]

I think you mean synthetic division, which is just a faster method of doing things, same result though

Yeah that's it. Would it be worth it learning that method?

[psyxwar]

Yeah that's it. Would it be worth it learning that method?

It'll probably take you like a minute to learn, so why not?

[Bluegirl]

I'm not getting anywhere with these.
(5x+6)/4 = (100-4x)/(3) -6


6/(x) + 4 = 15/(x) - 3.
With this i keep getting 7/9 instead of 9/7 so I must be multiplying the wrong thing.
Can someone note the steps to see where I went wrong?

(sorry that I'm bad at writing equations out)

[clueless123]

a)

Spoiler

etc

b)

Spoiler

[Bluegirl]

a)

Spoiler

etc

b)

Spoiler

Thanks

[alchemy]

How important is learning matrices? Is it necessary to know it for other topics?

It's usually just briefed over in most schools. It's that thing that you learn when you only come across it, which I like

[Nato]

hey guys, having some trouble with dilations.

one question was state the transformation which maps the graphs of   to

for:  to
now i did


and therefore it has been dilated by a factor of 5 from the x-axis. Well, according to the book, my answer is correct. But could someone please provide me with an intuitive and/or more efficient way of solving this.

i also need some assistance with to

thank-you

[soNasty]

Find the third solution to the equation
if it is known that -2 and 5 satisfy the equation

[mackintosh]

Find the third solution to the equation
if it is known that -2 and 5 satisfy the equation

Are you sure there isn't an x cubed somewhere ? As it is written there should only be  two solutions

[nhmn0301]

hey guys, having some trouble with dilations.

one question was state the transformation which maps the graphs of   to

for:  to
now i did


and therefore it has been dilated by a factor of 5 from the x-axis. Well, according to the book, my answer is correct. But could someone please provide me with an intuitive and/or more efficient way of solving this.

i also need some assistance with to

thank-you

Hi,
af(x)    Dilation factor of a, parallel to y-axis (from x-axis)
f(ax)    Dilation factor of 1/a, parallel to x-axis(from the y-axis)
f(1/x) Dilation factor of a, parallel to x-axis (from y axis)
so for your question, just apply the same methods above: to will be a dilation of factor (5)^1/2 from the x-axis.
Hope this helps.

[soNasty]

Are you sure there isn't an x cubed somewhere ? As it is written there should only be  two solutions

Sorry!! It's

[brightsky]

Let P(x) = 3x^3 + ax^2 - 33x - b.
P(-2) = 4a - b + 42 = 0.........(1)
P(5) = 25a - b + 210 = 0.......(2)

Solve (1) and (2) simultaneously:
a = -8 and b = 10

So, P(x) = 3x^3 - 8 x^2 - 33x - 10 = (x+2)(x-5)(3x+1)

Therefore, the other solution to the equation P(x) = 0 is x = -1/3.

[Only Cheating Yourself]

Just make sure you learn them in the right order. Quadratics first, cubics second, quartics third, ...
Also make sure you know what a polynomial is and isn't before you start off. Makes life easier later on.

Yea but if i know a poloynimal is how will that help me?  Isn't a polynomial any number/expression that does not have a negative power?  even 3 is a polynomial because u can write it as 3x^0 so the degree is 0.

[brightsky]

Pretty much!

A polynomial is essentially any function which can be written in the following form:

P(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_2 x^2 + a_1 x + a_0

where a_n, a_(n-1), ..., a_2, a_1, a_0 are all real number constants and n is a non-negative integer.

Bear in mind that n cannot be infinity. Technically, a function like sin(x) can be expressed as a power series, but it nevertheless is not a polynomial since it does not have a 'highest power' (i.e. degree). Also bear in mind that the degree of 0 (which is a polynomial) is undefined, not 0.

[Only Cheating Yourself]

Pretty much!

A polynomial is essentially any function which can be written in the following form:

P(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_2 x^2 + a_1 x + a_0

where a_n, a_(n-1), ..., a_2, a_1, a_0 are all real number constants and n is a non-negative integer.

Bear in mind that n cannot be infinity. Technically, a function like sin(x) can be expressed as a power series, but it nevertheless is not a polynomial since it does not have a 'highest power' (i.e. degree). Also bear in mind that the degree of 0 (which is a polynomial) is undefined, not 0.

The p(x)=…….  What does that actually mean am i suppose to memorise that?