Final answer:
To find the coefficient of x³ after multiplying two polynomials and combining like terms, multiply the coefficient of x³ in the first polynomial by the constant term in the second polynomial, resulting in -21 for this case.
Step-by-step explanation:
The student has asked about the coefficient of x³ when two polynomials are multiplied and like terms are combined. To find this coefficient, we multiply the polynomials x⁴ - 3x³ + 5² - 6x + 1 and 2x³ - 3x² + 4x + 7. The coefficient of x³ in the first polynomial is -3, and in the second polynomial, we only consider the constant term, which is 7, as the product of these two will result in a term with x³. Thus, -3 multiplied by 7 gives us the coefficient of x³, which is -21.