Results 1 to 2 of 2

Math Help - Remainder and Factor Theorem HELP

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    10

    Exclamation Remainder and Factor Theorem HELP

    well i missed a week off school, and i am completely in the dark on my homework, if someone could please tell me what to do it would be GREATLY appreciated
    1. The function f is given by f(x) = 2x 3 + x 2 13x + 6.
    (a) Find f(2), f() and f(2).
    (i) Write down the remainder when f(x) is divided by x + 2.
    (ii) Explain why 2x 1 is a factor of f(x).
    (b) Factorise f(x) and hence solve f(x) = 0.
    (c) Sketch the curve y = f(x).

    2. Factorise p(x) = 13x - 6 - 4x 3. HINT you may have to divide for this one!
    Solve p(x) = 0.
    Sketch the graph of y = 13x - 6 - 4x 3.

    3. (a) Use the remainder theorem to find the remainder when x 3 2x 2 + 8x 3 is divided by x 5.
    (b) When x 3 4x 2 + ax + 6 is divided by x 3 the remainder is 18.
    Find the value of the constant a.

    4. When x 3 + px 2 + qx + 1 is divided by x 2 the remainder is 9 and when divided by x + 3
    the remainder is 19. Find the values of the constants p and q.

    5. Find the value of the constant k given that x + 4 is a factor of f(x), where
    f(x) = 3x 3 + 10x 2 kx - 4.
    Hence factorise f(x) and solve f(x) = 0.


    in general i have no idea what f(x) means, is it something times what x is, please please help me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2008
    Posts
    147
    f(x) is the given function. I'll try to help you with the first one, and hopefully you'll understand how to do it from there.
    a.)
    f(x) = 2x^3 + x^2 -13x + 6
    f(-2) = 2(-2)^3 +(-2)^2 -13(-2) +6 Plug in -2 whenever you see x

    f(-2) = -16 +4 +26+6 = 20, might be off on the arithmetic
    Do the same for the other values, just plug in the given value whenever you see a x and simplify.
    i.)
    Polynomial Long Division

    Here is a website that shows you how to do polynomial long division.
    ii.)
    If there is no remainder, than the divisor is a factor of the entire polynomial. (e.g. 24/3 = 8, no remainder, so 3 is a factor)
    b.)
    To factor the polynomial, you divide it by its factors, and you are already given one. Divide first by (2x-1), and you will get a quadratic equation of the form ax^2 + bx + c , and that should be simply to factor.

    Once you have it all factored, say it turns out to be something like (2x-1)(x+3)(x-2). Set this equal to 0, and solve for x
     <br />
(2x-1)(x+3)(x-2) = 0<br />
This is only true when any one of the factors is 0,so you have
    2x-1=0
    x+3=0
    x-2=0

    Solving these for x, we see that x = 1/2, -3, 2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factor/Remainder theorem
    Posted in the Algebra Forum
    Replies: 7
    Last Post: December 2nd 2009, 04:27 AM
  2. Factor & Remainder Theorem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: November 29th 2009, 04:33 AM
  3. remainder & factor theorem
    Posted in the Algebra Forum
    Replies: 4
    Last Post: July 24th 2009, 07:17 AM
  4. Factor and remainder theorem
    Posted in the Algebra Forum
    Replies: 0
    Last Post: June 27th 2009, 11:47 PM
  5. Remainder and Factor Theorem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 21st 2007, 06:00 AM

Search Tags


/mathhelpforum @mathhelpforum