Final answer:
The question referenced seems to have typos, and without the correct expressions, we cannot determine an equivalent polynomial. However, we can discuss the multiplication in scientific notation and the use of the quadratic formula to find the roots of a quadratic equation, as well as the application of the binomial theorem in series expansions.
Step-by-step explanation:
The polynomial expression presented has an initial multiplication of two numbers (24 - 36), which results in a negative number (-12) since 36 is larger than 24. The second part appears to involve algebraic terms, which may be variable expressions, but since there are potential typographical errors in the expression, a precise equivalent term cannot be provided without further clarification. An important note is that polynomial expressions can involve variables raised to non-negative integer exponents, constants, and arithmetic operations.
However, we can analyze the example provided about scientific notation. The process of multiplying the number 6.022 × 10²³ by 6.42 × 10⁻² would involve multiplying the coefficients (6.022 and 6.42) and then adding the exponents of 10 due to the properties of exponents in scientific notation, thereby obtaining an answer of 1.67 × 10·.
In another given example, a quadratic equation is mentioned with constants a, b, and c. To solve for the roots of the equation, we would employ the quadratic formula, which in general form is −b ± √(b² - 4ac) / (2a). This can be used to find the roots of any quadratic equation given the constants a, b, and c.
Lastly, it's crucial in mathematics to recognize that series expansions like the binomial theorem can greatly simplify the process of expanding polynomials raised to a power.