Maths Question

[bonrepos]

My grandson has sent me this maths question asking for help.

Sadly, I'm not sure how to understand how to get to the answer. Can anyone help,please?

The question

63x3 - 27x + 14x2 - 6x ? Answer ( x-x ) ( 7x-3 )

Thank you from an incompetent grandfather.

[dealtn]

My grandson has sent me this maths question asking for help.

Sadly, I'm not sure how to understand how to get to the answer. Can anyone help,please?

The question

63x3 - 27x + 14x2 - 6x ? Answer ( x-x ) ( 7x-3 )

Thank you from an incompetent grandfather.

Are you sure that's the question?

Where is the "="?

[Mike4]

My grandson has sent me this maths question asking for help.

Sadly, I'm not sure how to understand how to get to the answer. Can anyone help,please?

The question

63x3 - 27x + 14x2 - 6x ? Answer ( x-x ) ( 7x-3 )

Thank you from an incompetent grandfather.

I find this confusing due to the use of the "x" symbol to mean two different things. It seems to be used both as an unknown variable and as a multiplication sign. Could it be re-written as 63x3 - 27a + 14x2 - 6a Answer ( a-a ) ( 7a-3 )

But ewven that looks pretty meaningless to me. What IS the actual question?

[UncleEbenezer]

I find this confusing due to the use of the "x" symbol to mean two different things. It seems to be used both as an unknown variable and as a multiplication sign. Could it be re-written as 63x3 - 27a + 14x2 - 6a Answer ( a-a ) ( 7a-3 )

But ewven that looks pretty meaningless to me. What IS the actual question?

Taken literally that's trivial: a=217/33 (the "answer" term being zero). But as you say, it seems implausible.

Possible explanations other than mere miscommunication include a kiddie winding up his grandpa, or an incompetent teacher. Or ....

[mc2fool]

Similarly along the are you sure that's the question lines, could the 3 and 2 actually be cubed and squared? So 63x³ - 27x + 14x² - 6x ?

And "Answer ( x-x ) ( 7x-3 )" is clearly problematic as, whichever way you look at it, ( x-x ) is going to be zero ...

But do I understand this correctly .. he's been given both the question and the answer ... and so, the actual "test" is to show the workings of how to get from the former to the latter?

BTW, it'd be useful for folks to know how old your grandson is ...

[Dod101]

It would also help if there were some brackets in the original question.

Dod

[stewamax]

Is grandson in year 4 of the Cambridge Maths Tripos ? - which may be why the question itself is intentionally unintelligible to those of little brain like me ...

[GrahamPlatt]

Isn’t this (9x^2 + 2x)(7x - 3) ?

[scotia]

My grandson has sent me this maths question asking for help.

Sadly, I'm not sure how to understand how to get to the answer. Can anyone help,please?

The question

63x3 - 27x + 14x2 - 6x ? Answer ( x-x ) ( 7x-3 )

Thank you from an incompetent grandfather.

I fear something has gone wrong in the copying of the problem.
If we assume that the question is - what are the roots of the equation 63x3 - 27x +14x2 - 6x = 0
Then although it is a cubic, there is a common factor of x, so one solution is x = 0
This leaves a quadratic equation 63x2 + 14x - 33 = 0 with two roots. This is easily solved, but the solutions do not include (7x-3) = 0, as can be seen by plugging x = 3/7 into the quadratic equation.
Try to get a hold of the original question

[bonrepos]

Thank you for all your replies so far.

My grandson is 19 and the maths test is one part of tests in order for him to gain entry to a government organisation (no not MI5!)

He has now sent me a copy of the original question which is below

63x2 - 27x + 14x2 - 6x = ?

The question has multiple choice answers which are

1. x(7x-3)x(7x - 3)
2. (x-x) (7x - 3)
3. (0) (7x-3)
4. (7x-3)
5. (x2-1) (7x-3) : x2 is squared

The answer is No2 but why?
Yes the question might be squared and cubed. There are no brackets aroud any numbers in the basic question.

[Mike4]

Isn’t this (9x^2 + 2x)(7x - 3) ?

Well the OP certainly falls into the category of "This is the answer, now what is the question?" doesn't it?

It has the look and feel of a quadratic equation to me, but with errors in the transcription somewhere.

[Boots]

Isn’t this (9x^2 + 2x)(7x - 3) ?

Well, that's what I think, but it does presuppose quite a few changes to the original question.

[GrahamPlatt]

Thank you for all your replies so far.

My grandson is 19 and the maths test is one part of tests in order for him to gain entry to a government organisation (no not MI5!)

He has now sent me a copy of the original question which is below

63x2 - 27x + 14x2 - 6x = ?

The question has multiple choice answers which are

1. x(7x-3)x(7x - 3)
2. (x-x) (7x - 3)
3. (0) (7x-3)
4. (7x-3)
5. (x2-1) (7x-3) : x2 is squared

The answer is No2 but why?
Yes the question might be squared and cubed. There are no brackets aroud any numbers in the basic question.

Ah, now I understand. You’ll be wanting a political answer… not my field, sorry.

[scotia]

Thank you for all your replies so far.

My grandson is 19 and the maths test is one part of tests in order for him to gain entry to a government organisation (no not MI5!)

He has now sent me a copy of the original question which is below

63x2 - 27x + 14x2 - 6x = ?

The question has multiple choice answers which are

1. x(7x-3)x(7x - 3)
2. (x-x) (7x - 3)
3. (0) (7x-3)
4. (7x-3)
5. (x2-1) (7x-3) : x2 is squared

The answer is No2 but why?
Yes the question might be squared and cubed. There are no brackets aroud any numbers in the basic question.

OK - This is entirely different from the original. We no longer have an x cubed. So it is a simple quadratic equation
63x2 - 27x +14x2 - 6x = 77x2 -33x = 11x(7x-3)
And the solutions of 11x(7x - 3) =0 are x=0 and 7x-3 = 0 - i.e. x=3/7

[Mike4]

Thank you for all your replies so far.

My grandson is 19 and the maths test is one part of tests in order for him to gain entry to a government organisation (no not MI5!)

He has now sent me a copy of the original question which is below

63x2 - 27x + 14x2 - 6x = ?

The question has multiple choice answers which are

1. x(7x-3)x(7x - 3)
2. (x-x) (7x - 3)
3. (0) (7x-3)
4. (7x-3)
5. (x2-1) (7x-3) : x2 is squared

The answer is No2 but why?
Yes the question might be squared and cubed. There are no brackets aroud any numbers in the basic question.

OK - This is entirely different from the original. We no longer have an x cubed. So it is a simple quadratic equation
63x2 - 27x +14x2 - 6x = 77x2 -33x = 11x(7x-3)
And the solutions of 11x(7x - 3) =0 are x=0 and 7x-3 = 0 - i.e. x=3/7

I think we'd all have got there a lot sooner had any of us been able to incorporate superscript into our posts!

(Edit to add the missing word.)

[mc2fool]

Thank you for all your replies so far.

My grandson is 19 and the maths test is one part of tests in order for him to gain entry to a government organisation (no not MI5!)

He has now sent me a copy of the original question which is below

63x2 - 27x + 14x2 - 6x = ?

The question has multiple choice answers which are

1. x(7x-3)x(7x - 3)
2. (x-x) (7x - 3)
3. (0) (7x-3)
4. (7x-3)
5. (x2-1) (7x-3) : x2 is squared

The answer is No2 but why?
Yes the question might be squared and cubed. There are no brackets aroud any numbers in the basic question.

OK - This is entirely different from the original. We no longer have an x cubed. So it is a simple quadratic equation
63x2 - 27x +14x2 - 6x = 77x2 -33x = 11x(7x-3)
And the solutions of 11x(7x - 3) =0 are x=0 and 7x-3 = 0 - i.e. x=3/7

I think we'd all have got there a lot sooner had any of us been able to incorporate superscript into our posts!

Some of us did. But I don't see how the above gets to supposed answer (2) ...

[Alaric]

So it is a simple quadratic equation
63x2 - 27x +14x2 - 6x = 77x2 -33x = 11x(7x-3)

Might be clearer to write it the way it was done in FORTRAN and BASIC with * meaning multiply and ** meaning exponentiate.


Thus 63*x**2 - 27*x + 14*x**2 - 6x simplifying to 77*x**2 - 33*xx simplifying to 11*x*(7*x-3)

Or use the exponent symbol (shift 6) and write it as

63x^2 -27x+14x^2-6x

[Mike4]

Some of us did.

Oh yes, so you did, my apologies!

How do superscripts work please? We were discussing it on another forum and could not do it as the old way had been disabled in a software upgrade - found to a be some sort of security risk IIRC.

[Mike4]

But I don't see how the above gets to supposed answer (2) ...

On further consideration I agree with you. It doesn't.

The question, clarified by the OP is 63x2 - 27x + 14x2 - 6x = ?

This strikes me as unsolvable without more info. Others have assumed 63x2 - 27x + 14x2 - 6x = 0 and have gone on to solve it as a quadratic but it isn't, as far as my plumbery maths goes. They are actually asking what 77x2 - 33x is equal to, so it is not safe to assume it is zero. So how would one go about solving it? I don't think it is possible without more info. Possibly this is why it is a multi-choice question, we can plug in each answer offered as a simultaneous equation and seef* it works.

Seef: verb, invented by my kids, a contraction of "see if".

[Breelander]

How do superscripts work please?

You can use the Alt key and the numeric keypad to insert any character in a post, ALT+0178 gives the superscript ²

This is the complete reference list, in table format, of the original set of Windows ALT Codes for special characters, signs and symbols such as ™ © ♥ Ñ € ¢ £ ½ ♂ ♀ ¥ ☻ ♪. ALT codes are keyboard shortcuts for quickly inserting non-ASCII special characters and symbols that are not included on normal computer keyboard characters and keyboard symbols

https://altcodeunicode.com/