Chapter R - Section R.5 - Polynomials - R.4 Assess Your Understanding - Page 49: 93

Quotient = $\quad 4x-3$ Remainder = $\quad x+1$

$\begin{array}{llllll} & 4x & -3 & & & \\ & -- & -- & -- & -- & \\ x^{2} \ \ ) & 4x^{3} & -3x^{2} & +x & +1 & \\ & 4x^{3} & & & & \\ & -- & -- & -- & -- & \\ & & -3x^{2} & +x & +1 & \\ & & -3x^{2} & & & \\ & & -- & -- & -- & \\ & & & +x & +1 & \\ & & & & & \end{array}$ Check: $(x^{2})(4x-3)+(x+1)=$ $=4x^{3}-3x^{2}+x+1$