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Math Help - Find a polynomial of degree 3 with real coefficients that satisfies...

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    Find a polynomial of degree 3 with real coefficients that satisfies...

    Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.?

    Zeros of -3,-1, 4, and P(2) = 5

    I am attempting this problem in order to study for an upcoming test. I am stuck on this one, and would really like to learn if someone could please assist me, I would very much appreciate it.
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    Re: Find a polynomial of degree 3 with real coefficients that satisfies...

    I have multiplied (x + 3)(x+1)(x-4)
    to get x^3 - 13x -12
    Where do I go from here?
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    Re: Find a polynomial of degree 3 with real coefficients that satisfies...

    Quote Originally Posted by SammyAbby View Post
    I have multiplied (x + 3)(x+1)(x-4)
    to get x^3 - 13x -12
    Where do I go from here?
    P(x) = k(x+3)(x+1)(x-4)

    5 = k(2+3)(2+1)(2-5)

    solve for k
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    Re: Find a polynomial of degree 3 with real coefficients that satisfies...

    Thank you for your assistance...I am still a bit confused...my book says that the answer is P(x) = (-x^3/6) + (13x/6) + 2
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    Re: Find a polynomial of degree 3 with real coefficients that satisfies...

    How did they get this?
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    Re: Find a polynomial of degree 3 with real coefficients that satisfies...

    P(x) = k(x+3)(x+1)(x-4)

    5 = k(2+3)(2+1)(2-4)

    5 = -30k

    k = -\frac{1}{6}

    P(x) = k(x+3)(x+1)(x-4)

    P(x) = -\frac{1}{6}(x+3)(x+1)(x-4)

    P(x) = -\frac{1}{6}(x^3-13x-12)

    P(x) = -\frac{x^3}{6} + \frac{13x}{6} + 2
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