Melody

I put a great deal of time into this answer Frosty and I do want a response from you..

Gamemaster,

You need to start talking about the questions that you post.

I mean you need to discuss what you already think you know and what thoughts you have on the rest.

Just dumping questions is simply NOT cool.

I think you are capable of better.  

Have you tried drawing this.  You will not get it without a picture.

You will end up with a half a big circle and a quarter of 2 little circles.     the area of a circl is pi*r^2

Try if for yourself

Note that the other answer already given is incorrect.

Find a polynomial f(x) of degree 5 such that both of these properties hold: f(x) is divisible by x^3.

and   f(x)+2 is divisible by (x+1)^3

Write your answer in expanded form (that is, do not factor f(x)

\(f(x)=x^3(ax^2+bx+c)\\ g(x)=f(x)+2=x^3(ax^2+bx+c)+2\\ g(-1)=0\quad so\\ -1(a-b+c)+2=0\\ -a+b-c+2=0\\ \boxed {c=2+b-a}\\ g(x)=x^3(ax^2+bx+2+b-a)+2\\ g(x)=ax^5+bx^4+(2+b-a)^3+2\\ \)

Next I divided that by  x+1 and got

\(h(x)=ax^4+(b-a)x^3+2x^2-2x+2\)

I know h(x) must also be diviasable by (x+1)    so  h(-1)=0

h(-1)=a(1)+(b-a)(-1)+2(1)-2(-1)+2

h(-1)=a+(-b+a)+2+2+2

h(-1)=2a-b+6 =0

b=2a+6

\(h(x)=ax^4+(2a+6-a)x^3+2x^2-2x+2\\ h(x)=ax^4+(a+6)x^3+2x^2-2x+2\\\)

Now I divided that by   (x+1)^2 = x^2+2x+1

And put the remainder = 0 hence solving for a.

I will leave you do the grunt work and some of the finishing up.

Note: This method does work but there may be a quicker way.

Hi Frosty,

Welcome back to the forum. :)

Why have you included all that unrendered latex?

You should make it as easy as possible for people to read and interpret your questions. 

Beats me ... any ideas.

Please include the address of the original question.

Ok thanks, that makes sense :)

What figure.

If you are going to copy stuff then cite where it comes from and include everything that is needed.

Assuming you mean  y=  1/4  *  x   =  (1/4)x    which is the same as    x/4  then

y = (1/4) of -12 = -3