UKC

My daughter is doing her maths homework and we are stuck on "factorising", please could someone tell me how to factorise 8x^2 - 56x + 64?

In reply to Gill187:

http://www.tiger-algebra.com/drill/8x~2-56x64/

May help?

In reply to mattrm:

Thank you I will take a look at that.

In reply to Gill187:

Factor out 8 (all divisible by 8), then you are left with 8(x^2 - 7x + 8)

At this point it can't be factorised further I think, unless the + and - are the wrong way.

In reply to Gill187:

As in solve the quadratic by factorising? You can't with that one unless I am mistaken.

In reply to Gill187:

Are you sure it's not 8x^2 - 56x - 64? Because often homework questions are meant to be factorise nicely, and that goes to (x+8)(8x-8).

In reply to Gill187:

I agree with the others - It looks like a misprint in the signs if the quadratic is to factorise.

If you type factor 8x^2 + 56x - 64 into the website wolfram alpha it will show you the answer. It's a good way to check what you've done. (note I've swapped the signs).

Good luck with the factorisation.

In reply to climbwhenready:

Yes. Assuming that, the full explanation goes as follows.

First up, spot that there's a common factor of 8 in all the coefficients, so you can change it to
8(x^2 -7x - 8).
Now, you're trying to get this into the form 8(x + A)(x + B).

There are two approaches:
1) use the quadratic formula to tell you that
(x^2 -7x - 8) = 0 iff x = (7 +/- 9)/2 = (-1 or 8) and hence if (x^2 -9x + 8) = (x + A)(x + B) then A and B have to be 1 and -8.
Or
2) (normally easier for simpler equations) just look at it and think that since
(x+A)(x+B) = x^2 + (A+B)x + A*B = x^2 -7x -8, you know that A*B = -8 and A + B = -7
Since this is a homework example, they're probably going to be fairly simple whole numbers, so try a few values, and you'll rapidly get to the same answer, viz
8x^2 - 56x + 64 = 8(x+1)(x-8).
If the "try a few" approach doesn't succeed, fall back on the formula.

In reply to Ramblin dave:

Yeah, I got the signs wrong in my answer

In reply to Gill187:

Isn't it factoring?

In reply to Gill187:

I just can't believe that you joined UKC to ask a Math(s) question. I know UKC is supposed to be the font of all knowledge, but when someone joins just to ask a specific educational question that tells you something about the people we have in our midst. I'm guessing that it is only a matter of time before Gooooogle is not the first place people turn to for answers.

In reply to Gill187:

I only looked at this thread out of curiosity to see what kind of maths question it might be.

I don't even understand what factorising or factoring is.

But I would be interested in knowing whether it has any practical use? Or is it simply an academical theory?

In reply to Dave Perry:



Yes. Factorising is an important part of algebra. Algebra is the language of mathematics. Mathematics is the language of much of science. Science drives technology. Technology drives the economy.

Factorising is also, of course, fun in itself.

In reply to Robert Durran:

Sounds like a good answer to me!!

In reply to Gill187:

Start with your formula 8x^2 - 56x + 64
Extract the common factor (8) as per 'crayefish at 15:10 Wed'
8(x^2 - 7x + 8)

Then find two numbers that when ...
- added together make -7,
- and when multiplied together give +8

Hence,the three factors of 8x^2 - 56x + 64 are
8, (x - 1.43884472) and (x - 5.5615528)

[to 7 decimal places at least!]

In reply to Dave Perry:


It allows you to find roots of equations etc. So for example, if something can be modelled by the equation y = x^2 + 2x + 1 = (x+1)(x+1). You can see it has roots where x = -1.

Factorising can also help you separate fractions etc which can help integration and differentiation. This can then be used to find areas, rates of change etc...

Plus many more uses also

In reply to Markgoesclimbing:

Mmmmmmaaaaaattttttthhhhhhhhssssss!!!!!!!!!!!!!!


Yeeeeaaaaahhhhhhh!!!!!

Maths is great.