91Ó°ÊÓ

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$x^{4}-2 x^{3}-20 x^{2}-8 x-96=0 \quad\left(r_{1}=6, r_{2}=-4\right)$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(x^{5}-3 x^{3}+5 x^{2}-10 x+6\right) \div(x+2)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$2 x^{4}-19 x^{3}+39 x^{2}+35 x-25=0 \quad(5 \text { is a double root })$$

Solve the given equations without using a calculator. $$9 x^{4}-3 x^{3}+34 x^{2}-12 x=8$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(3 x^{4}-12 x^{3}-60 x+4\right) \div(x-0.5)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$4 n^{4}+28 n^{3}+61 n^{2}+42 n+9=0 \quad(-3\text { is a double root) }$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$6 x^{4}+5 x^{3}-15 x^{2}+4=0 \quad\left(r_{1}=-\frac{1}{2}, r_{2}=\frac{2}{3}\right)$$

Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$8 x^{3}+2 x^{2}-32 x-8, x-2$$

Solve the given equations without using a calculator. $$D^{5}+D^{4}-9 D^{3}-5 D^{2}+16 D+12=0$$

Solve the given equations without using a calculator. $$x^{6}-x^{4}-14 x^{2}+24=0$$