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Math Help - algebra

  1. #1
    Junior Member
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    May 2008
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    algebra

    determine the value k so that x-4 is a factor of x^2+8x+k
    i know that answer is going o be 12, i got it by dividing x-4 into x^2+8x+k but im not sure about the remainder, bcz i got k+48
    does that change the answer.

    m^2-k^2+6k-9 has a factor of (m-k+3) what is the other
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  2. #2
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    x^2+8x+k to factor this with (x-4) being a factor we would get (x-4)(x+y)= x^2+(-4+y)x-4y and since the coefficients have to match up, (-4+y)=8 and -4y=k

    From (-4+y)=8 we see y=12, so -4(12)=-48=k
    and you can see that x^2+8x-48=(x-4)(x+12)

    m^2-k^2+6k-9=m^2-(k^2-6k+9)=m^2-(k-3)^2 which is the difference of two perfect squares and x^2-y^2=(x-y)(x+y) so m^2-(k-3)^2=(m-(k-3))(m+(k-3))=(m-k+3)(m+k-3)
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