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    The cubic polynomial x^3 +ax^2 +bx -8 where a and b are constants has factors (x+1) and (x+2) find a and b

    So i used the factor therom if (x-a) is a factor then f(a) is a factor to say that -1 and -2 are factors i then tried to do divson of polynomials but got really confused. Is this even the correct way to go about this question?
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    i would expand out (x+1)(x+2)(x-a) and simply compare coeffs (you can work out what the a is ridiculously simply). probably not the most elegant way of doing it but it'll work
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    (Original post by hazbaz)
    The cubic polynomial x^3 +ax^2 +bx -8 where a and b are constants has factors (x+1) and (x+2) find a and b

    So i used the factor therom if (x-a) is a factor then f(a) is a factor to say that -1 and -2 are factors i then tried to do divson of polynomials but got really confused. Is this even the correct way to go about this question?
    Easy way: put -1 and -2 in to form a pair of simultaneous equations and then solve for a and b, so you will have two equations, both in terms of a and b (one that you substituted -2 into and one that you substituted -1 into).
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    Well +1, +2 and another number have to multiply to make -8. So that means the other number must be -4. So the cubic equation looks like: (x+1)(x+2)(x-4) - just expand this and compare the coefficients of each.
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    (x+1) and (x+2) are factors, which mean they divise without remainders thus, (x+1) = 0 and (x+2) = 0, so we can take form this x = -1 and x = -2.

    For x = -1, -1 + a - b + 8 = 0 ---> a -b +7 = 0
    For x = -2, -8 + 4a - 2b -8 = 0 ---> 4a - 2b - 16 = 0

    Solve simultaneously. (Sorry if I've made any silly maths errors, but you get the jist)
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    (Original post by hazbaz)
    The cubic polynomial x^3 +ax^2 +bx -8 where a and b are constants has factors (x+1) and (x+2) find a and b

    So i used the factor therom if (x-a) is a factor then f(a) is a factor to say that -1 and -2 are factors i then tried to do divson of polynomials but got really confused. Is this even the correct way to go about this question?
    Okay so if it has those factors , you can do it simultaneously.

    Sub in x=-1 as the roots, then obtain 2 equations. As the following:
    f(-1) = -1^3 +a(-1)^2 +b(-1) -8 = 0
    f(-2) = -2^2 + a(-2)^2+b(-2)-8=0

    Multiply it out cleanly, then move the constant to the right side to get 2 easy simultaneous equations
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    hey i made a video tutorial for this question on my blog. You can find the link in the signature. look for factor theorem question with unknowns. Hope that helps
 
 
 
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