#1
Got inspired by the homework threads to do some work. Anyway, how does x3-7x+9 factorise? The small text is meant to be an index.
#2
I don't think it does....
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#3
um you sure it's x to the 3?
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#5
Are you only asked to factorise it?

Edit never mind you answered.
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#6
It doesn't
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#7
You can't use the quadratic equation on a cubic polynomial.
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#8
Quote by Craig_241
Are you only asked to factorise it?

Edit never mind you answered.


There's two parts to the question, the first asks you to factorise it, then the second asks you to find the greatest value for k, a straight line parallel to the y-axis that intersects it at three points. I've got the answer for the second part, and I think the answer they wanted for the first part was doesn't factorise.
#9
Quote by MidnightSonata
You can't use the quadratic equation on a cubic polynomial.


Ah, then I've got a wrong answer. What should I do then? I've got the full question in the above post.
#10
it goes down to x(x^2-7)+9. thats just the next step. do what you like with that one
#13
Quote by kidwizz88
it goes down to x(x^2-7)+9. thats just the next step. do what you like with that one


You can't factor out the x because it's not a common factor in all the parts of the equation. If it were also with the 9 this would work perfectly. But that factorization is incorrect.

Since it's a cubic equation there are going to be at least 3 roots. Once you find one root, it'll simplify to a quadratic and you can use the quadratic formula from there.
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#14
no, ive only taken the x out of the parts that has x. i realise that 9 doesnt contain x so i have left that there. the x() only multiplies what is in the brackets by x. not the x.
#15
...a line parallel to the y axis can't intersect a function in more than one place.
i'll assume you meant X-axis, in which case the highest value of k would be <16.1285

as for factoring...i don't see how you'd do it by hand but the X intercept (which is what factoring is meant to solve for if you didn't know) is near -3.141

that's a really strange question considering nothing you would've learned so far applies to it.
#16
Quote by kidwizz88
no, ive only taken the x out of the parts that has x. i realise that 9 doesnt contain x so i have left that there. the x() only multiplies what is in the brackets by x. not the x.


Yeah, but if you factor out x, it has to factor out of all the parts of the equation. Since x is not with the 9, it can't be factored out of the other two parts.


This equation does, in fact, factor out, but not to any nice numbers.

(x + 3.1409233)(x^2 - 3.1409233x + 2.8653994)
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#17
the line of the equation x^3 -7x+ 9 is a cubic line. so the line of k from the y axis will intersect this line at 3 points. you just have to find where.
#18
kidwiz88 is right about the first factoring step. you can simplify it to x(x^2-7)+9...it just really doesn't do you much good.

the factoring midnightsonata posted shows the only root at -3.141 that i said.

and kidwizz, he said a line parallel to the y axis. a vertical line can't intersect a function more than once.
#19
yes it can, if that function is shaped appropriately. and for the roots, you get some really funky numbers. i dunno, i cant be bothered to think about maths when i dont need to. got enough of that in the day
#20
only one root.

a horizontal line can intersect a function more than once, but not a vertical line. that's pretty much the definition of a function...
#21
*sees thread*

*is disappointed with content*

it doesn't factorise nicely. full stop. you don't need to factorise when the roots are nasty.

the fact he says "a function" kidwizz means it can't intersect more than once because the formal definition of a "function" is that it can't have 2 different y values for the same x value.
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#22
Quote by BluesLP1990
...a line parallel to the y axis can't intersect a function in more than one place.
i'll assume you meant X-axis, in which case the highest value of k would be <16.1285

as for factoring...i don't see how you'd do it by hand but the X intercept (which is what factoring is meant to solve for if you didn't know) is near -3.141

that's a really strange question considering nothing you would've learned so far applies to it.


Yeah, I did mean the X-axis. Thanks for all the help guys. Can I asked how you arrived at that answer? I actually forgot to mention that it asked for an integer answer, and I arrived at 16 anyway, I'd just like to know how you solved that.
#23
x cubed minus seven x plus nine?

it doesn't factor.
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