A polynomial function is a function that is a sum of terms that each have the general form ax n, where a and n are constants and x is a variable. If a function has a local maximum at a, then [latex]f\left(a\right)\ge f\left(x\right)[/latex] for all x in an open interval around x = a. A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial.The terms can be: Constants, like 3 or 523.. Variables, like a, x, or z, A combination of numbers and variables like 88x or 7xyz. Because a height of 0 cm is not reasonable, we consider only the zeros 10 and 7. We can use this graph to estimate the maximum value for the volume, restricted to values for w that are reasonable for this problem, values from 0 to 7. In other words, it must be possible to write the expression without division. Theai are real numbers and are calledcoefficients. We can estimate the maximum value to be around 340 cubic cm, which occurs when the squares are about 2.75 cm on each side. The shortest side is 14 and we are cutting off two squares, so values w may take on are greater than zero or less than 7. A quadratic equation is a second degree polynomial having the general form ax^2 + bx + c = 0, where a, b, and c... Read More High School Math Solutions – Quadratic Equations Calculator, Part 2 Using technology to sketch the graph of [latex]V\left(w\right)[/latex] on this reasonable domain, we get a graph like the one above. With quadratics, we were able to algebraically find the maximum or minimum value of the function by finding the vertex. Rational Root Theorem The Rational Root Theorem is a useful tool in finding the roots of a polynomial function f (x) = … So, if it's possible to simplify an expression into a form that uses only those operations and whose exponents are all positive integers...then you do indeed have a polynomial equation). If you need to solve a quadratic polynomial, write the equation in order of the highest degree to the lowest, then set the equation to equal zero. The most common types are: 1. This means we will restrict the domain of this function to [latex]0