18x^3+51x^2+26x+15
Decartes' Rule of signs says there are no positive roots.
The Rational Roots Theorem says that the rational roots must be of the form
±(1,3,5)/(1,2,3,6)
You can quickly see that there are no rational roots, so a numeric method is your only choice left.
What was your question, anyway?
The expression you provided is a polynomial of degree 3. It can be written in expanded form as:
18x^3 + 51x^2 + 26x + 15
To evaluate this polynomial, you need to substitute a value for x and simplify the expression.
For example, if you want to evaluate the polynomial for x = 2, you substitute x = 2 into the expression:
18(2)^3 + 51(2)^2 + 26(2) + 15
Simplifying each term, you get:
18(8) + 51(4) + 26(2) + 15
144 + 204 + 52 + 15
Combine the like terms:
= 415
Therefore, when x = 2, the polynomial expression evaluates to 415.
You can evaluate the polynomial for different values of x by substituting the desired value into the expression and following the same steps.