Find a polynomial with a degree of 3 and zeros -3,3,5

f(x) = x³ - 5x² - 9x + 45

Step-by-step explanation:

Given x = a, x = b are the zeros of a polynomial, then

(x - a), (x - b) are the factors and f(x) is the product of the factors.

Here the zeros are x = - 3, x = 3 and x = 5, thus

(x + 3), (x - 3) and (x - 5) are the factors and

f(x) = (x + 3)(x - 3)(x - 5) ← expand the first pair of factors using FOIL

     = (x² - 9)(x - 5) ← distribute

    = x³ - 5x² - 9x + 45

wheres graph

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.