Final answer:
The polynomial is in standard form, which is option (a) 2x³ - 4x² + 7x - 1. For quadratic equations, one uses the quadratic formula given by -b ± √(b² - 4ac) / (2a) to find the solutions.
Step-by-step explanation:
The polynomial 2x³ - 4x² + 7x - 1 is already written in standard form. Standard form for polynomials requires that terms be listed in descending order of their powers. So, the correct representation of the given polynomial in standard form is 2x³ - 4x² + 7x - 1, corresponding to option (a).
When solving quadratic equations of the form ax² + bx + c = 0, you can use the quadratic formula to find the roots. The quadratic formula is given by -b ± √(b² - 4ac) / (2a), where a, b, and c are coefficients from the quadratic equation. Here is how you would rearrange and solve for x using a quadratic equation as an example.To rewrite the polynomial 2x³ - 4x² + 7x - 1 in standard form, we arrange the terms in descending order of exponents:2x³ - 4x² + 7x - 1So, the polynomial in standard form is 2x³ - 4x² + 7x - 1 (option a)