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16 December, 06:30

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, - 5).

Write the equation of this cubic polynomial function.

Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?

-5

The linear factors of the cubic are

+1
Answers (1)
  1. 16 December, 06:46
    0
    Zeros are the x values which make the function equal to zero. Set it up as you would for a binomial with a constant multiplier "k" to account for the y-intercept (0, - 5) given.

    f (x) = k (x-2) (x-3) (x-5)

    Use the y-intercept (0,-5) to solve for k.

    -5 = k (0-2) (0-3) (0-5)

    -5 = - 30k

    -5/-30 = k

    1/6 = k

    The cubic polynomial function is then ...

    f (x) = (1/6) (x-2) (x-3) (x-5)

    Linear factors are the linear (line) expressions you can factor out of the polynomial. They are (x-2), (x-3) and (x-5).
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