Question

Use long division to find the quotient and remainder when f(x)=9 x^5 - 1 x^4 - 1 x^3 - 1 x^2 - 3 x - 5 is divided by g(x)=9 x^2 - 6 x + 4.

Answer 1

f(x)/g(x)

Rewrite the expression in long division form (9x⁵ - x⁴ - x³ - x² - 3x - 5)/(9x²- 6x + 4).

Divide the first term of the dividend by the first term of the divisor 9x⁵/9x²= x³.

So, the first term of the quotient is x³. Multiply (9x²- 6x + 4) by x³ and subtract.

Divide the first term of the last row by first term of the divisor 5x⁴/9x² = 5x²/9

So,the second term of the quotient is 5x²/9. Multiply (9x²- 6x + 4) by 5x²/9 and subtract.

Divide the first term of the last row by first term of the divisor  (-5x³/3)/9x² = - 5x/27.

So,the third term of the quotient is (- 5x/27). Multiply (9x²- 6x + 4) by (- 5x/27) and subtract.

Divide the first term of the last row by first term of the divisor (- 39x²/9)/9x² = -39/81.

So,the fourth term of the quotient is - 39/81. Multiply (9x²- 6x + 4) by (- 39/81) and subtract.

Quotient is

And the remainder is

.