Question

Find s and r if (x + 3) is a factor of sx³ + rx² - 28x + 15 and has a remainder of -60 when divided by (x - 3).

Answer 1

$$s(-3)^3+r(-3)^2-28(-3)+15=0$$

$$-9s+3r+28+5=0$$

$$3s-r=11$$

$$s(3)^3+r(3)^2-28(3)+15=-60$$

$$9s+3r-28+25=0$$

$$3s+r=1$$

$$\begin{matrix} 3s-r=11 \\ 3s+r=1 \end{matrix}$$

$$\begin{matrix} r=3s-11 \\ 6s=12 \end{matrix}$$

$$\begin{matrix} s=2 \\ r=-5 \end{matrix}$$