Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−8x²+x+2; between 2 and 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. See Examples 3 and 4.

$\text{ƒ}\left(x\right)=-3x^4-5x^3+2x^2$

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = x² - 4x + 3

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x³(x²-4)(x-1)

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -2x² - 8x - 7

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x⁴+x³-6x²-7x-2

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x² + 18x + 1

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=3x⁴-7x³-6x²+12x+8