Perform the division: $6 x^{3} - 23 x + x^{2} + 12$ by $2 x - 3$

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Solution

Steps: 1) Rearrange the polynomial with higher degree to smaller power.It is shown in the figure as well.
2) Multiply $(2 x - 3)$ with $3 x^{2}$ , to get $6 x^{3}$ , Remainder $= 10 x^{2} - 23 x$
3) Multiply $(2 x - 3)$ with $5 x$ , to get $10 x^{2}$ , Remainder $= - 8 x + 12$
4) Multiply $(2 x - 3)$ with $- 4$ to get $- 8 x$ , Remainder $= 0$

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