How would i solve and graph 2x^3-4x^2-5x+1=0 ?

See image below

Solving the Equation Graphically

Using the graphing calculator, put in the formula. When the function touches or goes through the x-axis are the solutions to this equation.

Solving the Equation

I don't know how to solve a cubic, so I use the factor theorem. If I use a positive number, I get a negative answer. So I try a negative numbers, starting with -1. Using -1, the result is 0, so (x-(-1)) or (x+1) is a factor. Knowing (x+1) is a factor, we can divide it into the equation using long division. When I do this, I get 2x^2-6x+1 as a quotient. I couldn't factor this over integers, so I used the quadratic formula to get the roots of (3+/-root(7))/2.

Graphing

Now we have the 3 zeros of the equation, we can sketch the function. Now we need to know what the function does at the extremes. If we put a large negative number in for x, y will be a larger negative number. Similarly, if we put a large x value, we will get a larger positive number.

Good luck,

Paul