consider the polynomial y = x^4 + 4x^3 - 2x^2 + 40x - 120
a)graph the polynomial and use it to identify any x-intercepts
b)list the factors that correspond to the x-intercepts you found
c) write the equation of the polynomial in factored form
To graph the polynomial y = x^4 + 4x^3 - 2x^2 + 40x - 120, we can look at the x-intercepts which occur when y = 0:
a) Setting y = 0, we get x^4 + 4x^3 - 2x^2 + 40x - 120 = 0. Using a graphing calculator or software, we can see that the x-intercepts are at x = -5, -3, 2, and 4.
b) The factors corresponding to the x-intercepts are (x + 5), (x + 3), (x - 2), and (x - 4).
c) Writing the equation in factored form:
y = (x + 5)(x + 3)(x - 2)(x - 4)