Long Division?

Question

Use long division to find the quotient and remainder when
f(x)=-4 x^5 + 8 x^4 - 2 x^3 + 5 x^2 + 4 x - 4
is divided by
g(x)=9 x^2 + 5 x + 7.

Answer 1

The function is .

Divide the first term of the dividend by the first term of the divisor -4x⁵/9x²= -4x³/9

So, the first term of the quotient is -4x³/9. Multiply (9x²+ 5x + 7) by -4x³/9 and subtract.

Divide the first term of the last row by firsy term of the divisor (92x⁴/9)/9x² = 92x²/81

So,the second term of the quotient is 92x²/81. Multiply (9x²+ 5x + 7) by 92x²/81 and subtract.

Divide the first term of the last row by first term of the divisor  (-370x³/81)/9x² = - 370x/729.

So,the third term of the quotient is (- 370x/729). Multiply (9x²+ 5x + 7) by (- 370x/729) and subtract.

Divide the first term of the last row by first term of the divisor (- 301x²/729)/9x² = -301/6561.

So,the fourth term of the quotient is (-301/6561). Multiply (9x²+ 5x + 7) by (-301/6561) and subtract.

Therefore Quotient is

Remainder is .