To find an equivalent expression for the function f(x) = x³ + 2x², we can start by analyzing the given polynomial. This expression is a combination of two terms: the cubic term x³ and the quadratic term 2x².
We can factor the expression to see if it can be simplified. First, we notice that both terms share a common factor of x². Thus, we can factor that out:
f(x) = x²(x + 2).This rewriting shows that the function can be expressed as the product of x² and (x + 2). This factorization makes it easier to understand the behavior of the function, such as finding roots or analyzing its growth.
Therefore, the equivalent expression for f(x) can be stated as x²(x + 2), which retains the same values as the original function across all x values.