Question

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

Answer 1

Use the zeroes to determine the roots.

Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.

Use the y-intercept (0, –5) to solve for the leading coefficient.

Substitute the leading coefficient into the polynomial function for a and simplify.

Answer 2

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).