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Math Help - Factored form question

  1. #1
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    Factored form question

    How do you make "-5(t^2)+10t+35" into factored form?
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  2. #2
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    Quote Originally Posted by sinjid9 View Post
    How do you make "-5(t^2)+10t+35" into factored form?

    First you take out a common factor of -5 leaving

     -5t^2+10t+35 = -5(t^2-2t-7)

    Now I would complete the square inside the brackets.

    -5(t^2-2t-7)

    You take the coeffeicent of the linear term, half it then square it.

    \left( \frac{-2}{2}\right)^2 = (-1)^2 = 1 giving

    -5((t^2-2t{\color{red}+1})-7{\color{red}-1})

    -5((t-1)^2-8)

    -5((t-1)^2-(\sqrt{8})^2)

    Now applying the difference of 2 squares and we are finished.

    -5(t-1-\sqrt{8})(t-1+\sqrt{8})
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  3. #3
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    in the part:

    how do you know where to put the brackets that seperate (+1) and (-7)
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  4. #4
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    In -5(t^2-2t-7) I was looking for a new constant term that would help me make a perfect square. Finidng +1 as this term gave

    -5((\underbrace{t^2-2t{\color{red}+1}}_{\text{perfect square}})-7{\color{red}-1})

    I couldn't just throw away the -7 and to balance the equation I introduced an extra -1 from the +1 found.

    A perfect square has the from of either

    a^2-2ab+b^2 = (a-b)^2 or a^2+2ab+b^2 = (a+b)^2
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  5. #5
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    k one more question. If I were to make this into an equation like this
    "h=-5(t^2)+10t+35" is it possible to make "h=-5(t^2)+10t+35" into a(x-s)(x-t)? Without graphing it?
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  6. #6
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    Quote Originally Posted by sinjid9 View Post
    "h=-5(t^2)+10t+35" is it possible to make "h=-5(t^2)+10t+35" into a(x-s)(x-t)? Without graphing it?

    Do you mean h=-5t^2+10t+35= a(t-b)(t-c)

    If so h=-5t^2+10t+35=-5(t-1-\sqrt{8})(t-1+\sqrt{8}) from post #2.
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