Which expression is equivalent to 7 minus 2 z minus 4 times open bracket z cubed minus the fraction with numerator z cubed plus 4 z squared plus 11 z plus 14 and denominator z plus 2 close bracket ?

Divide the fraction’s numerator by z + 2: (z³ + 4z² + 11z + 14) ÷ (z + 2) = z² + 2z + 7. The expression in brackets becomes z³ − (z² + 2z + 7) = z³ − z² − 2z − 7. Distributing −4 and combining with 7 − 2z gives −4z³ + 4z² + 6z + 35, which is choice A.

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