Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    7
    ReputationRep:
    Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by Sniper21)
    Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
    Guess a root and factorise. A good start is to plug in factors of the constant term.
    Online

    21
    ReputationRep:
    Factor theorem says that if f(a)=0 then (x-a) is a factor and since this is a cubic f(x)=(x-a)(bx^2+cx+d)=x^3+2x^2-5x-6.Find a suitable a(try factors of -6) and then equate coefficients to find b,c and d and then factorise the quadratic.
    Offline

    3
    ReputationRep:
    (Original post by Sniper21)
    Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
    Is that all the information that is given?
    Offline

    13
    ReputationRep:
    (Original post by Sniper21)
    Given that f(x) = x^3 = 2x^2 - 5x - 6 use the Factor Theorem to factorise f(x) completely, hence solve the inequality x^3 + 2x^2 - 5x - 6 > 0
    I'm doing additional maths gcse this year and have self taught this so I'm gonna give it a go, no guarantees that it will be correct.

    By substituting values in for x I can see that f(2) = 0
    So (x-2) is one of the three brackets
    Then we divide f(x) by (x-2)
    x^3+2x^2-5x-6 = (x-2) + x^2+4x+4
    f(x) = (x-2)(x+1)(x+3)
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by RDKGames)
    Guess a root and factorise. A good start is to plug in factors of the constant term.
    This is the first part of the question
    Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

    Please show me the step by step solution.
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by leadheadsmith)
    Is that all the information that is given?
    No, this is the original question:
    Use the remainder theorem to find the remainder when f9x) = 8x^3 - 4x^2 +6x+7 is divided by x-1
    • Community Assistant
    Offline

    18
    ReputationRep:
    (Original post by Sniper21)
    This is the first part of the question
    Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

    Please show me the step by step solution.
    The remainder of a polynomial f(x) when divided by (x-a) is f(a), so you would replace any x in f(x) with an a. Step by step solutions are not allowed.
    • Community Assistant
    • Welcome Squad
    Online

    20
    ReputationRep:
    (Original post by Sniper21)
    This is the first part of the question
    Use the Remainder Theorem to find the remainder when f(x) = 8x^3 - 4x^2 + 6x +7 is divided by x-1

    Please show me the step by step solution.
    These basics should be covered in the C1 book shouldn't they?

    Just plug in x=1 and your output is the remainder.
    Offline

    3
    ReputationRep:
    (Original post by Sniper21)
    No, this is the original question:
    Use the remainder theorem to find the remainder when f9x) = 8x^3 - 4x^2 +6x+7 is divided by x-1
    8x^2+4x+10

    x-1 | 8x^3 - 4x^2 +6x+7
    -(8x^3-8x^2)
    4x^2+6x+7
    -(4x^2-4x)
    10x+7
    -(10x-10)
    17

    Remainder = 17

    I think it's right, i find these questions easier written down haha
    • Thread Starter
    Offline

    7
    ReputationRep:
    (Original post by RDKGames)
    These basics should be covered in the C1 book shouldn't they?

    Just plug in x=1 and your output is the remainder.
    This is what I got for part a) Remainder theorem:
    polynomial f(x) has remainder r when divided by (x-a) if f(a) = r
    f(x) = 8x^3 - 4x^2 + 6x + 7
    f(x) = 8 - 4 + 6 + 7 = 17
    It is very straightforward, thanks a lot for your help!
    Offline

    3
    ReputationRep:
    (Original post by Sniper21)
    This is what I got for part a) Remainder theorem:
    polynomial f(x) has remainder r when divided by (x-a) if f(a) = r
    f(x) = 8x^3 - 4x^2 + 6x + 7
    f(x) = 8 - 4 + 6 + 7 = 17
    It is very straightforward, thanks a lot for your help!
    No worries Don't forget to give us all the information in future though!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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