Solve using polynomial long division and please show work: (5x^4 + 21x^3+ 5x^2- 9x - 6)/(5x^2 + 6x + 2)

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  x² +3x -3 +3x/(5x² +6x +2)

Step-by-step explanation:

As with any long division, you formulate a partial quotient, then subtract the product of that and the divisor from the dividend. The result is a new dividend. You're done when the degree of the dividend is less than the degree of the divisor.

The partial quotient term is simply the ratio of the highest-degree terms in the dividend and the divisor. (That is what makes it easier than numerical long division.)

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step-by-step explanation: