Divide: $7 x^{4} + 4 x^{2} + 3 x - 5$ by $2 x^{2} + 3 x - 2$

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Solution

Steps:
1) Multiply $(2 x^{2} + 3 x - 2)$ with $\frac{7}{2} x^{2}$ , to get $7 x^{4}$ , Remainder $= - \frac{21}{2} x^{3} + 11 x^{2} + 3 x - 5$
2)Multiply $(2 x^{2} + 3 x - 2)$ with $- \frac{21}{4} x$ , to get $- \frac{21}{2} x^{3}$ , remainder $= \frac{107}{4} x^{2} - \frac{15}{2} x - 5$ ,
3) Multiply $(2 x^{2} + 3 x - 2)$ with $\frac{107}{8}$ to get $\frac{107}{4} x^{2}$ , remainder $= - \frac{381}{8} x + \frac{87}{4}$

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