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Math Help - solving polynomial word problems

  1. #1
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    solving polynomial word problems

    if anyone could help with any of these questions, it would really make my day!

    question 1. When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. determine the values of m and n.

    question 2. A rectangular prism has dimensions 10cm by 10cm by 5cm. when each dimension is increased by the same amount, the new volume 1008 cm. what are the dimensions of the new prism?

    question 3. The distance, d, in kilometers, travelled by a plane after t hours can be represented by d(t)=-4t^3+40t^2+500t, where 0<t<10. how long does the plane take to fly 4088km?
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  2. #2
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    Quote Originally Posted by extraordinarymachine View Post
    if anyone could help with any of these questions, it would really make my day!

    question 1. When the polynomial mx^3-3x^2+nx+2 is divided by x+3, the remainder is -1. When it is divided by x-2, the remainder is -4. determine the values of m and n.
    for f(x) = mx^3-3x^2+nx+2

    then f(-3)=-1 and f(2)=-4


    so for f(-3)=-1 we get

    f(-3) = m(-3)^3-3(-3)^2+n(-3)+2

    -1 = m(-3)^3-3(-3)^2+n(-3)+2


    and for f(2)=-4 we get

    f(2) = m(2)^3-3(2)^2+n(2)+2

    -4 = m(2)^3-3(2)^2+n(2)+2

    simplify these equations and solve them simultaneously
    Last edited by pickslides; May 26th 2009 at 02:02 PM. Reason: typo
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  3. #3
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    Quote Originally Posted by extraordinarymachine View Post
    question 2. A rectangular prism has dimensions 10cm by 10cm by 5cm. when each dimension is increased by the same amount, the new volume 1008 cm. what are the dimensions of the new prism?
    The new dimensions are increased by the same amount, lets call that 'x'

    so the equation becomes (10+x)(10+x)(5+x)= 1008

    Can you solve it from here?
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  4. #4
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    Quote Originally Posted by extraordinarymachine View Post

    question 3. The distance, d, in kilometers, travelled by a plane after t hours can be represented by d(t)=-4t^3+40t^2+500t, where 0<t<10. how long does the plane take to fly 4088km?

    for this equation d(t)=-4t^3+40t^2+500t you have 2 variables distance and time so as 4088km is a distance put this into the equation replacing d(t).

    4088=-4t^3+40t^2+500t

    4t^3-40t^2-500t+ 4088=0

    you need to solve for t from this point. Take out 4 as a common factor
    t^3-10t^2-125t+ 1022=0

    now use the factor theorem which says

    If f(a)=0 then (x-a) is a factor
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