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?-5The linear factors of the cubic are
Accepted Solution
A:
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).