Question 199449
I assume you meant {{{2x^4 - 5x^3 - 24x^2 - 7x + 10}}}

You are told two roots are -2 and 1/2

First use this URL --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit
Divide the given polynomial by {{{x+2}}}  since {{{x+2}}} as a factor means -2 is a solution.

That yields a result with no remainder. So, x-2 is in fact a root.

Now take the result from this division and divide that by {{{x - 1/2}}}

That also divides without a remainder. Take the quotient of that division, which is a quadratic, and solve it using the methods you have already learned. (factoring, quadratic equation, etc)