Find the quotient the and remainder of the following division:
$(5 x^{3} - 8 x^{2} + 5 x - 7) \div (x - 1)$

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Solution

Steps:
1) Multiply $(x - 1)$ with $5 x^{2}$ , to get $5 x^{3}$ , remainder $= - 3 x^{2} + 5 x$
2) Multiply $(x - 1)$ with $- 3 x$ , to get $- 3 x^{2}$ , Remainder $= 2 x - 7$ ,
3) Multiply $(x - 1)$ with $2$ , to get $2 x - 7$ , Remainder $= - 5$
Quotient $= 5 x^{2} - 3 x + 2$ , remainder $= - 5$

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