Final answer:
The first term of the polynomial is -2x⁴ after rearranging the terms in descending order by exponent. Key mathematical strategies include algebraic manipulation, using formulas, simplifying expressions, and verifying the reasonableness of the solution.
Step-by-step explanation:
The student is asking about terms in a polynomial. The first term in the given polynomial 2x³+3-2x⁴+7x-x² is -2x⁴, as polynomials are usually written with terms in descending order of their exponents. However, in the provided expression, the terms are not in the standard order. To identify the first term, reorder the polynomial: -2x⁴ + 2x³ - x² + 7x + 3. Now, the first term is clear.
When dealing with polynomials and equations such as quadratic equations, algebraic manipulation and simplification are essential. For example, completing the square or using the quadratic formula to find the roots of ax² + bx + c = 0, simplifying expressions, or rearranging terms in an equation are crucial steps towards solving mathematical problems effectively.
Additional strategies like checking the reasonableness of an answer and eliminating terms wherever possible can greatly assist in simplifying and solving algebra problems.