Final answer:
To find when the polynomial 2x³+3x²-3x-2 is greater than or equal to zero, a calculator may be necessary to identify the roots and determine the intervals that satisfy the inequality. This process is akin to calculating non-integer exponents, like 3¹.⁷, where calculators can easily find the value.
Step-by-step explanation:
The task at hand is to determine when the polynomial 2x³+3x²-3x-2 is greater than or equal to zero. To solve this inequality, one would typically factor the polynomial, if possible, and then use a sign chart or test values in each interval to find when the polynomial is nonnegative. Given the complexity of the polynomial, factoring may not be straightforward, and the use of a graphing calculator or another computational tool might be necessary to find the exact roots or to provide an approximate solution. Using a calculator to find when the inequality is satisfied is analogous to handling expressions with non-integer exponents, such as 3¹.⁷. Calculators can easily evaluate expressions with non-integer exponents, and in the context of inequalities, they can help us find the intervals where the polynomial remains nonnegative by identifying the roots and changes in the sign of the polynomial. If we are given that one value is larger than another, such as 'adding 1 must be larger than 1 + 1 = 2' or that 'one-third is smaller than one-half, thus their sum must be smaller than 1', this logic helps bound our inequality solutions with known quantities—though, in this case, it's not directly applicable to solving polynomial inequalities without specific numerical context.