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

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).