Which is a factor of x2-8x+15?

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  • Como answered 6 years ago
(x - 5)(x - 3)

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  • The VC 06 answered 6 years ago
    Hi,

    Good Question! Notice that the 15 here is from the product of two numbers when multiplied would give 15. Also, these two numbers when added together give us -8. Thinking about this, we need to recall the factors of 15 include: 1, 3, 5 and 15.

    At this point, I'm sure you're thinking of the two factors -3 and -5 which is a very good observation!

    Therefore we can say the following:

    ( x - 3 ) ( x - 5 ) <=== FINAL ANSWER

    * NOTE: As a check, you can use the FOIL Method on this binomial to get the Quadratic Expression that you were originally presented with! =)

    I hope that helps you out! Please let me know if you have any other questions!

    Source(s):

    College Calculus Student ; Math Tutor
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  • John S answered 6 years ago
    The question is likely: Factor x^2 - 8 x + 15.

    1) You have a quadratic expression
    the form of:
    Ax^2 + Bx + C

    2) You want to find the numbers p,q,r,s such that
    Ax^2 + B x + C = (p x + q )( r x + s)

    where the right hand side here is the factored form of
    the original expression.

    3) So multiply out (px + q)(rx + s)
    p x + q
    r x + s
    _____________
    (pr) x^2 + (rq + sp) x + qs

    4) We compare this general form to the one they gave
    you, so for your problem
    p r =1
    (rq + sp) =-8
    qs = 15

    5) A good guess would be to take p=r=1, so the second
    term becomes
    (q + p) = -8
    Think about numbers that when multiplied together
    give 15. These are:
    (1)(15) = 15
    (-1)(-15) = 15
    (3)(5) = 15
    (-3)(-5)=15

    6) Remembering that p+q = -8
    it looks like p=-3 and p=-5 will fit the bill.
    So in factored form you have
    (x - 3)(x - 5)

    7) Check the answer
    x - 3
    x - 5
    --------
    x^2 - (3 + 5)x + 15
    = x^2 - 8 x + 15

    so, there you go.
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  • seed of eternity answered 6 years ago
    Question Number 1 :
    For this equation x^2 - 8*x + 15 = 0 , answer the following questions :
    A. Calculate the Roots ( x1 and x2 ) !
    B. Use factorization to find the root of the equation !

    Answer Number 1 :
    The equation x^2 - 8*x + 15 = 0 is already in a*x^2+b*x+c=0 form.
    So we can imply that the value of a = 1, b = -8, c = 15.

    1A. Calculate the Roots ( x1 and x2 ) !
    Use abc formula and you get either
    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) or x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
    As we know that a = 1, b = -8 and c = 15,
    we just need to subtitute the value of a,b and c in the abc formula.
    Which produce x1 = (-(-8) + sqrt( (-8)^2 - 4 * (1)*(15)))/(2*1) and x2 = (-(-8) - sqrt( (-8)^2 - 4 * (1)*(15)))/(2*1)
    Which is can be turned into x1 = ( 8 + sqrt( 64-60))/(2) and x2 = ( 8 - sqrt( 64-60))/(2)
    Which is can be turned into x1 = ( 8 + sqrt( 4))/(2) and x2 = ( 8 - sqrt( 4))/(2)
    So we get x1 = ( 8 + 2 )/(2) and x2 = ( 8 - 2 )/(2)
    The answers are x1 = 5 and x2 = 3

    1B. Use factorization to find the root of the equation !
    x^2 - 8*x + 15 = 0
    <=> ( x - 5 ) * ( x - 3 ) = 0
    The answers are x1 = 5 and x2 = 3

    Source(s):

    This free Quadratic Solver should help you in the future :

    http://orimath.blogspot.com/search/label...
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  • 14years answered 6 years ago
    ha i'm studying this 2...

    Source(s):

    me meme
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  • Matt answered 6 years ago
    x=3, x=5
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  • MissLady_0318 answered 6 years ago
    Do you mean how to factor it? If that is what you mean, the answer is (x-5)(x-3)
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  • Cappucino answered 6 years ago
    x^2- 8x + 15
    x^2 - 3x - 5x - 15
    (x^2 - 3x) - (5x - 15)
    x(x - 3) - 5(x - 3)
    (x - 5)(x - 3)
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