Challenge question of polynomial ?

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  • 1 month ago

    The remainder from f(x) divided by a cubic has 2 as the highest power.

    The remainder from f(x) divided by (x-3) is 4, so it passes through (3,4).

    The remainder from f(x) divided by (x-2) is -1, so it passes through (2,-1).

    The remainder from f(x) divided by (x-1) is -4, so it passes through (1,-4)

    The remainder from f(x) divided by x is -5, so it passes through (0,-5), which is the vertex of the parabola. [The next point following the pattern of increasing consecutive odd differences is (-1,-4). 4--1=5, -1--4=3, -4--5=1 and -5-y=-1]

    The parabola with vertex (0,-5), vertical line of reflection and which passes though (3,4) is y = x² - 5, so the remainder is x² - 5.

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    Source(s): The quadratic equation of the curve with the vertex at (x₀,y₀), with a line of reflection parallel to the y axis and passing through (x₁,y₁) is y = (y₁-y₀)/(x₁-x₀)² (x-x₀)² + y₀.
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  • sepia
    Lv 7
    1 month ago

    A polynomial f(x) leaves a reminder -4, -1, and 4 

    when divided by x -1, x - 2, x - 3 respectively. Determine the reminder when f(x) is divided by (x^3 - 6x^2 + 11x - 6).

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