Question

1) Create your own polynomial function whose degree must be
higher than 2 and with rational zeros.
2) Find the following: (Show your complete solution.)
a. The y-intercept of your polynomial function.
b. The factored form of your polynomial function,
c. The zeros/ x-intercepts of your polynomial function using
synthetic division.
3) Construct your table of signs.
18​

Answer 1

Given : polynomial function whose degree must be  higher than 2 and with rational zeros.

To Find : Create  one  polynomial

The factored form of your polynomial function,

The zeros/ x-intercepts

The y-intercept

Solution:

P(x) = (x - 1)(x - 2)(x - 3)

Factored form =  (x - 1)(x - 2)(x - 3)

(x - 1)(x - 2)(x - 3) = (x - 1)(x² - 5x + 6)

= x³ - 5x² + 6x  - x²  + 5x - 6

= x³ - 6x² + 11x - 6

P(x) =  x³ - 6x² + 11x - 6

. The zeros/ x-intercepts are  1, 2 , 3

The y-intercept is  P(0) = 0 - 0 + 0 - 6 = - 6

y-intercept = - 6

P(x) =  x³ - 6x² + 11x - 6

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