What is the quotient and remainder if any when 4x to power four -x cubed plus 17x squared plus 11x plus 4 is divided by 4x plus 3 showing work?

(4x^4 - x³ + 17x² + 11x + 4) ÷ (4x + 3) = x³ - x² + 5x - 1 remainder 7.

Do the division via long division, looking at the highest power of x in the dividend:

_________________x³ ___- x²_ + 5x - 1

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4x + 3 | 4x^4 - x³ + 17x² + 11x + 4

_________4x^4 + 3x³ _____________________ ← x³(4x + 3); x³ in the quotient

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_______________- 4x³ + 17x² ______________ ← subtract and bring down next term (+ 17x²)

_______________ -4x³ __ -3x² ______________ ← -x²(4x + 3); - x² in the quotient

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______________________ 20x² + 11x ________ ← subtract and bring down the next term (+ 11x)

______________________ 20x² + 15x ________ ← 5x(4x + 3); + 5x in the quotient

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______________________________ -4x + 4 ____ ← subtract and bring down the next term (+ 4)

______________________________ -4x - 3 _____ ← -1(4x + 3); -1 in the quotient

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___________________________________ 7 ______ ← subtract; no more terms to bring down, this is remainder.