Divide Using Long Polynomial Division 12x^3+7x^2+9x+2 divided by 4x+1

Write the problem as a mathematical expression.

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

Divide the highest order term in the dividend ${\displaystyle 12x^3}$ by the highest order term in divisor ${\displaystyle 4x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 12x^3+3x^2}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Pull the next terms from the original dividend down into the current dividend.

Divide the highest order term in the dividend ${\displaystyle 4x^2}$ by the highest order term in divisor ${\displaystyle 4x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 4x^2+x}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Pull the next terms from the original dividend down into the current dividend.

Divide the highest order term in the dividend ${\displaystyle 8x}$ by the highest order term in divisor ${\displaystyle 4x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 8x+2}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.