Find the Remainder (x+4)÷(4x^4+18x^3+3x^2-18x+15)

$(x + 4) \div (4 x^{4} + 18 x^{3} + 3 x^{2} - 18 x + 15)$

Step 1

To calculate the remainder, first divide the polynomials.

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$4 x^{4}$

$18 x^{3}$

$3 x^{2}$

$18 x$

$15$

$x$

$4$

The final answer is the quotient plus the remainder over the divisor.

$0 + \frac{4 x^{4} + 18 x^{3} + 3 x^{2} - 17 x + 19}{4 x^{4} + 18 x^{3} + 3 x^{2} - 18 x + 15}$

Step 2

Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.

$4 x^{4} + 18 x^{3} + 3 x^{2} - 17 x + 19$