Divide [164x−84(x^2)−7(x^3)+17(x^4)+2(x^6)−72] by [12x+(x^3)−8]

Division of polynomials: Long Method (Shorter Version). Watch entirely the step-by-step process of finding the quotient of a degree-6 polynomial divided by a degree-3 polynomial. Both the Dividend and the Divisor here have missing power of x, respectively. Divide 164x-84(x^2)-7(x^3)+17(x^4)+2(x^6)-72 by 12x+(x^3)-8. The Dividend here is 84(x^2)-7(x^3)+17(x^4)+2(x^6)-72, while the Divisor is 12x+(x^3)-8.

Before anything else, always remember to arrange the power of x of the Dividend and the Divisor, respectively. Insert to the Dividend the missing power of x. Hence, the newly arranged Dividend here is 2(x^6)+0(x^5)+17(x^4)-7(x^3)-84(x^2)+164x-72 divided by the newly arranged Divisor here (x^3)+12x-8.

Here are the first few steps to begin the long method division of polynomials, divide the first term of the Dividend 2(x^6) by the first term of the Divisor (x^3) equals the first term of the Quotient 2(x^3), or 2(x^6)/(x^3) = 2(x^3). Next, the product of the first term of the Quotient 2(x^3) and the Divisor (x^3)+12x-8 equals Product1, or Product1 = 2(x^3)[(x^3)+12x-8] = [2(x^6)+24(x^4)-16(x^3)]. This Product1 is to be subtracted from the Divisor.

To continue this method, just perform the steps similarly as above. The division process ends until the difference between the last Dividend and the last Product becomes zero, otherwise, a remainder exists, in which its degree is lower than that of the divisor.

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