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

    1
    ReputationRep:
    I have these two questions:

    x(x+1)(2x+7) + 6(x+1)(x+3)

    and

    N^2(N+1)^2 + 4(N+1) ^3

    and just having started C1 am unsure how to solve them. The answers say they should become three brackets but I don't know how to form them without expanding everything, then I don't know where to go from there. Thanks for any help!
    • Community Assistant
    • Welcome Squad
    Offline

    20
    ReputationRep:
    Community Assistant
    Welcome Squad
    (Original post by mayjb)
    I have these two questions:

    x(x+1)(2x+7) + 6(x+1)(x+3)

    and

    N^2(N+1)^2 + 4(N+1) ^3

    and just having started C1 am unsure how to solve them. The answers say they should become three brackets but I don't know how to form them without expanding everything, then I don't know where to go from there. Thanks for any help!
    You can't solve them because they're not equations, that's not what you're doing most likely. Look to get them into a form where they're products of two factors. This means factor out common terms out of the whole expression.
    Offline

    10
    ReputationRep:
    (Original post by mayjb)
    I have these two questions:

    x(x+1)(2x+7) + 6(x+1)(x+3)

    and

    N^2(N+1)^2 + 4(N+1) ^3

    and just having started C1 am unsure how to solve them. The answers say they should become three brackets but I don't know how to form them without expanding everything, then I don't know where to go from there. Thanks for any help!
    For the first one notice that  (x+1) is both parts- this means that everything in that expression is multiplied by  (x+1) , and you can put it outside of brackets like with any other common factor.
    Rewrite it as:
     (x+1)(x(2x+7)+6(x+3))
    and see if you can do it from that.
    Offline

    3
    ReputationRep:
    (Original post by mayjb)
    I have these two questions:

    x(x+1)(2x+7) + 6(x+1)(x+3)

    and

    N^2(N+1)^2 + 4(N+1) ^3

    and just having started C1 am unsure how to solve them. The answers say they should become three brackets but I don't know how to form them without expanding everything, then I don't know where to go from there. Thanks for any help!
    In the first expression, there is a common factor of x+1, so take it out to give:
    (x+1)(x(2x+7) + 6(x+3)) = (x+1)(2x^2+13x+18) = (x+1)(x+2)(2x+9).

    In the second expression, there is a common factor of (N+1)^2, so take it out to give:
    (N+1)^2(N^2 + 4(N+1)) = (N+1)^2(N^2+4N+4) = (N+1)^2(N+2)^2.
    Offline

    12
    ReputationRep:
    Yes expand everything, then put in values of x between -3 and 3 (call this a) and if you find one that makes the equation equal zero, then (x-a) is a factor. Taking one factor out means you will be left with just a quadratic to factorise and that should leave three brackets! If you need any help I can do the working and put it on here if you wish
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by RDKGames)
    You can't solve them because they're not equations, that's not what you're doing most likely. Look to get them into a form where they're products of two factors. This means factor out common terms out of the whole expression.
    Yes sorry I meant factorize
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by HapaxOromenon3)
    In the first expression, there is a common factor of x+1, so take it out to give:
    (x+1)(x(2x+7) + 6(x+3)) = (x+1)(2x^2+13x+18) = (x+1)(x+2)(2x+9).

    In the second expression, there is a common factor of (N+1)^2, so take it out to give:
    (N+1)^2(N^2 + 4(N+1)) = (N+1)^2(N^2+4N+4) = (N+1)^2(N+2)^2.
    Ah I see thank you!
    • Thread Starter
    Offline

    1
    ReputationRep:
    (Original post by Uni12345678)
    Yes expand everything, then put in values of x between -3 and 3 (call this a) and if you find one that makes the equation equal zero, then (x-a) is a factor. Taking one factor out means you will be left with just a quadratic to factorise and that should leave three brackets! If you need any help I can do the working and put it on here if you wish
    Thank you, this method was what I saw online but i didn't understand what it meant so thanks!
 
 
 
  • 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
    Would you like to hibernate through the winter months?
    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.