Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    Write down the x values of the three points where the graph of y=x3-5x2-36x crosses the x-axis. Please help!!!
    Offline

    19
    ReputationRep:
    (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?
    Offline

    3
    ReputationRep:
    (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)
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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??
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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?
    Offline

    3
    ReputationRep:
    (Original post by JoeSugg)
    Do I need to use long division or something?
    Hint: \displaystyle x^3-5x^2-36x=x(x^2-5x-36)

    I'll include a solution in a spoiler. Only take a look to compare answers once you've solved the problem.
    Spoiler:
    Show
    \displaystyle y=x(x^2-5x-36)=x(x+4)(x-9)=0

    The three points are therefore (0,0), (-4,0) and (9,0). The x-intercepts are where y=0
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Dingooose)
    Hint: \displaystyle x^3-5x^2-36x=x(x^2-5x-36)

    I'll include a solution in a spoiler. Only take a look to compare answers once you've solved the problem.
    Spoiler:
    Show
    \displaystyle y=x(x^2-5x-36)=x(x+4)(x-9)=0

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

    What about this one..

    (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 😕
    Offline

    3
    ReputationRep:
    (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.
    Offline

    3
    ReputationRep:
    (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
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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? 😳
    Offline

    3
    ReputationRep:
    (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.
    Offline

    3
    ReputationRep:
    (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!

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

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

    Spoilers below:

    Spoiler:
    Show
    \displaystyle x^3+7x^2+2x-40=(x+5)(x^2+2x-8)=(x+5)(x+4)(x-2)

    Therefore the other factors are (x+4) and (x-2)
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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!

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

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

    Spoilers below:
    Spoiler:
    Show
    \displaystyle x^3+7x^2+2x-40=(x+5)(x^2+2x-8)=(x+5)(x+4)(x-2)

    Therefore the other factors are (x+4) and (x-2)
    Thank you so much, I think I'm starting to understand long division now. 😊
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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! 👍🏽
    Offline

    3
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (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. ☺️
    Offline

    3
    ReputationRep:
    (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.
    Offline

    19
    ReputationRep:
    (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.
    Offline

    3
    ReputationRep:
    (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.
 
 
 

University open days

  1. University of Bradford
    University-wide Postgraduate
    Wed, 25 Jul '18
  2. University of Buckingham
    Psychology Taster Tutorial Undergraduate
    Wed, 25 Jul '18
  3. Bournemouth University
    Clearing Campus Visit Undergraduate
    Wed, 1 Aug '18
Poll
How are you feeling in the run-up to Results Day 2018?
Useful resources

Study tools

Rosette

Essay expert

Learn to write like a pro with our ultimate essay guide.

Thinking about uni already?

Thinking about uni already?

See where you can apply with our uni match tool

Student chat

Ask a question

Chat to other GCSE students and get your study questions answered.

Creating

Make study resources

Create all the resources you need to get the grades.

Planner

Create your own Study Plan

Organise all your homework and exams so you never miss another deadline.

Resources by subject

From flashcards to mind maps; there's everything you need for all of your GCSE subjects.

Papers

Find past papers

100s of GCSE past papers for all your subjects at your fingertips.

Help out other students

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.