Math Is Fun Forum

I would expect 4 terms for that.

3^2 = 9     4^2 = 16  2x3x4 = 24,

Try a direct factorisation with two identical factors.

Bob

Good so far. Sum of cubes? Try it.

Bob

The quality of mercy is not strained.

Bob

They are the same but what did the question say?  Sometimes you're asked to factorise fully.  In an exam, read the question carefully to make sure of this point. If it doesn't say then either should get full marks.

Some years ago I did some A level marking for Ed-Excel. The first question asked candidates to do a certain bit of algebra (part A) and then to use the result to do something else (part B).  Other ways of doing this second part could have been used except for that crucial wording. The chief examiner told us to give no marks for part B to any candidate who didn't use part A. Along with other markers I was very unhappy about this but the chief's word is law so I did as told.

You'll be pleased to know that the standard of marking is very high. The mark scheme shows all the alternative ways that may earn marks and every bit gets working credit.  If we couldn't read a candidate's writing or had some other problem with awarding marks we had to send it on to our superviser, who also checked a sample of our marking.

I have to say, I only did it that once. It was very tedious and not how I wanted to spend my life. Useful insight though.

Bob

3 linear factors! I'd say that is fully done.

Bob

That's it done nicely.

Bob

Correct!

Bob

Ok. First notice that putting x=a causes x^5 - a^5 to become 0, so (x-a) is a factor => no remainder.
       
                                       x^4       + a   x^3       +    a^2 x^2   + a^3 x      + a^4
                  _____________________________________________________
x - a           |   x^5     + 0 x^4       + 0   x^3       +     0    x^2       + 0   x     - a^5
                      x^5      - a x^4
                     ______________
                                    a x^4        + 0   x^3
                                    a x^4        -a^2 x^3
                                   ___________________
                                                   + a^2 x^3       +    0    x^2
                                                   + a^2 x^3       -    a^3 x^2
                                                   _________________________
                                                                          +    a^3 x^2      + 0    x
                                                                          +    a^3 x^2      - a^4 x
                                                                          _____________________
                                                                                                   + a^4 x    - a^5

                                                                                                   + a^4 x    -  a^5
                                                                                                   _______________

                                                              remainder              =         0              0

so x^5 - a^5 = (  x^4       + a   x^3       +    a^2 x^2   + a^3 x      + a^4)(x-a)

Bob

Not me.  I did wonder about them though.  I count 6 missing. This forum has members from all over the world. That means a spread of politics and religion.  All posters need to think about this and take care with potentially controversial subjects.  But we do allow a wide range of topics so I was inclined to wait and see.  We had a poster a while back who started with an innocent statement but it provoked unpleasant responses so in the end we had to terminate it.

I recommend you stick to maths.

Bob

Where did that question spring from.

If r = 0.546189584... then a sphere's surface area = 4, so you cannot rule that out.

A cuboid 1 by 1 by 0.5 has surface area 4.

A cube with side 0.816497.... has surface area 4.

There are loads of possible shapes so there's not a lot you can say for certain.  A sphere has minimal surface area so you can probably say at least 1 dimension will be over the r given above.  You can probably get an upper bound for the shapes dimensions and I think that's about it.

A solid shape could certainly be a compound shape.

Bob

When I did my age 18 A levels, stats wasn't part of the course.

But it was introduced later and I had to teach it.  Sometimes I have to look up the methods.

Bob

p44 example 10 has (x-1). But the quesion here shows this can be generalised.

Bob