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# Factor Theorem Help :O watch

1. Write down the x values of the three points where the graph of y=x3-5x2-36x crosses the x-axis. Please help!!!
2. (Original post by JoeSugg)
Write down the x values of the three points where the graph of y=x3-5x2-36x crosses the x-axis. Please help!!!
You need to find the x values where y = 0.

So try factorising, can you see one factor immediately?
3. (Original post by JoeSugg)
Write down the x values of the three points where the graph of y=x3-5x2-36x crosses the x-axis. Please help!!!
What does the factor theorem suggest you do with this function? (Clue's in the name)
4. (Original post by Muttley79)
You need to find the x values where y = 0.

So try factorising, can you see one factor immediately?
Is the factor 0??
5. (Original post by ian.slater)
What does the factor theorem suggest you do with this function? (Clue's in the name)
Do I need to use long division or something?
6. (Original post by JoeSugg)
Do I need to use long division or something?
Hint:

I'll include a solution in a spoiler. Only take a look to compare answers once you've solved the problem.
Spoiler:
Show

The three points are therefore (0,0), (-4,0) and (9,0). The x-intercepts are where
7. (Original post by Dingooose)
Hint:

I'll include a solution in a spoiler. Only take a look to compare answers once you've solved the problem.
Spoiler:
Show

The three points are therefore (0,0), (-4,0) and (9,0). The x-intercepts are where
Thanks

(x + 5) is a factor of x 3 + 7x 2 + 2x - 40 Work out the other two linear factors of x 3 + 7x 2 + 2x - 40

I tried your method but it didn't work 😕
8. (Original post by JoeSugg)
Is the factor 0??
The factor theorem says that if (and only if) f(a) = 0 for some polynomial f and value a then (x-a) is a factor of f(x).

Be careful not to confuse a factor like (x-2) with a root where say f(2) = 0.

Because 0 is a root then (x-0) is a factor, which we would normally just write as x.

If you have to factorise a cubic or higher polynomial you can be sure that one of the roots is easy to find and then you do use long division ... which is trivial in this example.
9. (Original post by JoeSugg)

I tried your method but it didn't work 😕
Our replies crossed!

In this case you are given a factor of (x+5) so just do long division. And for practice you could work out what the corresponding root is and check that it works
10. (Original post by ian.slater)
Our replies crossed!

In this case you are given a factor of (x+5) so just do long division. And for practice you could work out what the corresponding root is and check that it works
The thing is...I kinda suck at long division when it comes to factor theorem..is there another way? 😳
11. (Original post by JoeSugg)
The thing is...I kinda suck at long division when it comes to factor theorem..is there another way? 😳
There are three methods to divide out a factor. One is long division. Explaining the other two in text is tricky ... try Googling polynomial long division and look for video clips ... Khan has some.

I always divide out at sight. But that takes practice.
12. (Original post by JoeSugg)
The thing is...I kinda suck at long division when it comes to factor theorem..is there another way? 😳
Algebraic long division is essentially just normal division but using algebra. Practise this because it's useful for problems like these. Otherwise, you can do a bit of guesswork. It's not hard for a simple problem like this one but it can be hard when dealing large coefficients. So learn algebraic division!

Play around and figure out what b and c are...

Spoilers below:

Spoiler:
Show

Therefore the other factors are and
13. (Original post by Dingooose)
Algebraic long division is essentially just normal division but using algebra. Practise this because it's useful for problems like these. Otherwise, you can do a bit of guesswork. It's not hard for a simple problem like this one but it can be hard when dealing large coefficients. So learn algebraic division!

Play around and figure out what b and c are...

Spoilers below:
Spoiler:
Show

Therefore the other factors are and
Thank you so much, I think I'm starting to understand long division now. 😊
14. (Original post by ian.slater)
There are three methods to divide out a factor. One is long division. Explaining the other two in text is tricky ... try Googling polynomial long division and look for video clips ... Khan has some.

I always divide out at sight. But that takes practice.
The Khan video actually helped.

Cheers! 👍🏽
15. (Original post by JoeSugg)
Thank you so much, I think I'm starting to understand long division now. 😊
What I showed you is not algebraic division. It's another technique that is much more limited.
16. (Original post by Dingooose)
What I showed you is not algebraic division. It's another technique that is much more limited.
Oh, well I tried long division using the Khan videos, checked with the spoilers and I almost got it right. ☺️
17. (Original post by JoeSugg)
Oh, well I tried long division using the Khan videos, checked with the spoilers and I almost got it right. ☺️
"Practise makes perfect" probably fits with mathematics more than any other subject. Keep practising and you will master the technique in no time.
18. (Original post by JoeSugg)
Oh, well I tried long division using the Khan videos, checked with the spoilers and I almost got it right. ☺️
Long division is not the best or quickest technique for these questions - people make too many errors.

(x + 5) is a factor of x 3 + 7x 2 + 2x - 40

Work out the other two linear factors of x 3 + 7x 2 + 2x - 40

I would say:

x^3+7x^2+2x-40=(x+5)(x^2+bx+c)

Then you know c instantly - or you can use the grid method for finding the quadratic.
19. (Original post by Muttley79)
Long division is not the best or quickest technique for these questions - people make too many errors.

(x + 5) is a factor of x 3 + 7x 2 + 2x - 40

Work out the other two linear factors of x 3 + 7x 2 + 2x - 40

I would say:

x^3+7x^2+2x-40=(x+5)(x^2+bx+c)

Then you know c instantly - or you can use the grid method for finding the quadratic.
That's the method that I showed as well. You would know c instantly AND you could quickly find b by doing the first half of the algebraic division in your head.

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