Which expression is equivalent to the fraction with numerator open paren 5 4th power of g plus 5 g cubed minus 17 g squared plus 6 g close paren minus open paren 3 4th power of g plus 6 g cubed minus 7 g squared minus 12 close paren and denominator g plus 2 ?
Answer
A
2 4th power of g minus g cubed minus 10 g squared plus 6 g plus 12
B
2 g cubed minus 5 g squared plus 6
C
2 4th power of g plus 11 g cubed minus 24 g squared plus 6 g minus 12
D
2 g cubed minus 5 g squared plus 18
Explanation
First subtract the polynomials in the numerator: (5g⁴ + 5g³ − 17g² + 6g) − (3g⁴ + 6g³ − 7g² − 12) = 2g⁴ − g³ − 10g² + 6g + 12. Dividing by g + 2 gives 2g³ − 5g² + 6, with remainder 0. So the equivalent expression is 2g³ − 5g² + 6, choice A.
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