Complete the following polynomial long division problem.

Question

Find the quotient, and the remainder. 4x^4+5x^2-7x+4 / (x+3)?

Answer 1

The expression is

Because there is no x³ - term in the dividend, we  need to line up the subtraction by using zero coefficients (or leaving spaces) for the missing terms.

Divide the first term of the dividend by the first term of the divisor 4x⁴/x = 4x³.

So,the first term of the quotient is 4x³. Multiply (x + 3) by 4x³ and subtract.

Divide the first term of the last row by first term of the divisor -12x³/x = -12x².

So,the second term of the quotient is -12x². Multiply (x + 3) by -12x² and subtract.

Divide the first term of the last row by first term of the divisor  (41x²)/x = 41x.

So,the third term of the quotient is 41x. Multiply (x + 3) by 41x and subtract.

Divide the first term of the last row by first term of the divisor (- 130x)/x = - 130.

So,the fourth term of the quotient is - 130. Multiply (x + 3) by (- 130) and subtract.

The remainder is the last entry in the last row.There fore, R = 394.

The number along the bottom row are the coefficients of the quotient.

The result of the division is (4x⁴ + 5x² - 7x + 4)/(x+3) = (4x³ - 12x² + 41x - 130)+ 394/(x+3).

The result of the division is 4x⁴ + 5x² - 7x + 4 = (x + 3)(4x³ - 12x² + 41x - 130) + 394.