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math urgent urgent urgent

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1)let f(x) be a polynomial function explian how to use the factor theorem to check if (x-c) is a factor of F(x)
2) use synthetic division to factor X^2-2x^2-9x+18 completly

  • math urgent urgent urgent -

    if f(c) = 0 , then x-c is a factor

    for f(x) = x^2 - 2x^2 - 9x + 18
    why do you have two x^2 terms, I will assume the first is x^3

    If so, we don't need the factor theorem for this one, grouping is obvious

    x^3 - 2x^2 - 9x + 18
    = x^2(x-2) - 9(x-2)
    = (x-2)(x^2 - 9)
    = (x-2)(x+3)(x-3)

    if you had not seen this, try x = ±1, ±2 , ±3 , that is factors of 18
    f(1) ≠ 0
    f(-1) ≠ 0
    f(2) = 0 , yeahhhh, so x-2 is a factor
    ..
    f(3) = 0 , so x-3 is a factor
    f(-3) = 0 , so x+3 is a factor

    since we have a cubic, there can only be a maximum of 3 algebraic factors
    so as above
    (x-2)(x+3)(x-3)

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