Question

What are the quotient and remainder when $3x^4-x^2$is divided by $x^3-x^2+1$?

Short answer

The quotient of dividing $3x^4-x^2$by $x^3-x^2+1$is$3x+3$and remainder$2x^2+3x-3$

Step-by-step solution

Step 1. Given data

The dividend is $3x^4-x^2$

The divisor is$x^3-x^2+1$

Step 2. use the long division method

Divide$3x^4-x^2$by$x^3-x^2+1$

$x^3-x^2+1\begin{array}{c}3x+3\end{array}\begin{array}{ccccc}3x^4& +\left(0\right)x^3& -x^2& +\left(0\right)x& +0\\ 3x^4& -3x^3& +0& +3x& +0\end{array}\begin{array}{ccccc}0& 3x^3& -x^2& +3x& +0\\ & 3x^3& -3x^2& +0& +3\end{array}\begin{array}{cccc}0& 2x^2& +3x& -3\end{array}$

further division is not possible

so quotient is $3x+3$

remainder$2x^2+3x-3$