Answer:
quotien is 2x² + 7x + 8 , remainder is 0
Explanation:
using long division
2x² + 7x + 4 ← quotient
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4x + 1 | 8x³ + 30x² + 23x + 4 → [ 8x³ ÷ 4x = 2x² ] multiply 4x + 1 by 2x²
8x³ + 2x² → [ subtract from line above ]
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0 + 28x² + 23x + 4 → [ 28x² ÷ 4x = 7x ] multiply 4x + 1 by 7x
28x² + 7x → [ subtract from line above ]
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0 + 16x + 4 → [ 16x ÷ 4x = 4 ] multiply 4x + 1 by 4
16x + 4 → [ subtract from line above ]
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0 0 ← remainder of zero
the quotient (2x² + 7x + 8 ) is a factor of the dividend