How to find all x-intercepts and y-intercepts of the graph of the function!

f(x)=2x^3-10x^2-8x+40

If there is more than one answer, separate them with commas.

Use synthetic division to lower the degree of the polynomial. Make it easier to factor and solve. You can try 2 for an initial guess that will work. I know cuz I plugged it into a calculator. After the division you should get 2x^2-6x-20. Set this equal to zero factor out a 2 and divide it across you get x^2-3x-10 factoring this further we achieve (x-5)(x+2)=0 thus you're other two solutions for x intercepts are 5 and -2. Don't forget about the initial solution, 2.
The y intercept occurs when all the x's in the equation are zero. Plugging 0 into the original equation we get y= 40

Since you have a function, you can have only 1 y intercept. If there were 2, it would fail the vertical line test.

To find the y intercept, the equation of the y axis is x = 0. So substitute 0 in for x. Then y = 40.

y intercept = (0, 40)

x intercepts. By the same rationale, the x axis is y = 0, so substitute 0 in for y (f(x) in this case)

0 = 2x^3 - 10x^2 - 8x + 40

Factor by grouping

2x^2(x-5) + (-8)(x-5) = (x-5)(2x^2 - 8) = 2(x-5)(x^2-4) = 2(x-5)(x+2)(x-2)

2(x-5)(x+2)(x-2) = 0.
By the zero factor rule, at least one of these factors must be 0

Then x = 5, -2, or 2

Then the x intercepts are (5,0), (-2,0), (2,0).

I hope this helps