Algebra 2 Polynomials and Rational Functions

A plane is going to fly 300 miles at a planned speed of 530 mph. The flight will have an average headwind of $$w$$ miles per hour the entire time, meaning the plane is flying directly against the wind. The time $$T$$ , in hours, of the flight is a function of the speed of the headwind $$w$$ , in mph, and can be modeled by $$T(w) = \frac{300}{530 - w}$$ . What does $$T(110)$$ mean in this situation?

At what value of $$w$$ does the graph have a vertical asymptote? Explain how you know and what this asymptote means in the situation.

There are many square prisms with volume 125 in³. Let $$w$$ represent the side length of the square base and $$h$$ represent the height in inches. Then the formula for the volume $$V$$ , in cubic inches, of these prisms is $$V=w^2h$$ and the equation for the surface area $$S$$ , in square inches, is $$S=2w^2+4wh$$ . Write an equation for $$S$$ as a function of $$w$$ when the volume of the prism is 125 in³. Explain or show your work.

The height of a softball, in feet, is modeled by the function $$h$$ given by $$h(t)=3+55t-16t^2$$ , where $$t$$ is the time, in seconds, after the softball is hit. A graph of the function is shown.

Let $$P$$ be a polynomial function, and $$P(x)=x^4-dx^3+8x^2-14x+16$$ . If $$(x-2)$$ is a factor of the polynomial, what is the value of $$d$$ ? Explain or show how you know.

Let $$g$$ be a polynomial function of $$x$$ where $$g(x)= 2x^3+5x^2-28x-15$$ . If $$(x-3)$$ is a factor of $$g$$ , write an equation for $$g$$ as the product of linear factors.

What are the zeros for the function y = x(x - 5)(x - 3)? Select all that apply.

Using the Fundamental Theorem of Algebra, what are all the factors of this polynomial: x⁵ - x⁴ + 6x³ - 6x² + 8x - 8