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what is the coefficient of x³ when x⁴-3x³ 5²-6x 1 is multiplied by 2x³ - 3x² 4x 7 and the like terms are combined?

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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.

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