Chapter 15

Find the roots of the given equations by inspection. $$(x+3)\left(x^{2}-4\right)=0$$

Find the roots of the given equations by inspection. $$x(2 x+5)^{2}\left(x^{2}-64\right)=0$$

Solve the given equations without using a calculator. $$2 x^{3}+5 x^{2}-x+6=0$$

Find the roots of the given equations by inspection. $$(x-5)\left(x^{2}+9\right)$$

Solve the given equations without using a calculator. $$x^{3}+2 x^{2}-5 x-6=0$$

Find the remainder by long division. $$\left(x^{3}+2 x-8\right) \div(x-2)$$

Find the roots of the given equations by inspection. $$\left(4 y^{2}+9\right)\left(25 y^{2}-10 y+1\right)=0$$

Solve the given equations without using a calculator. $$t^{3}-12 t-16=0$$

Find the remainder by long division. $$\left(x^{4}-4 x^{3}-x^{2}+x-100\right) \div(x+3)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$x^{3}-5 x^{2}+2 x+8=0 \quad\left(r_{1}=2\right)$$

Solve the given equations without using a calculator. $$3 x^{4}-x^{2}-2 x=0$$

Find the remainder by long division. $$\left(2 x^{5}-x^{2}+8 x+44\right) \div(x+1)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$R^{3}+1=0 \quad\left(r_{1}=-1\right)$$

Solve the given equations without using a calculator. $$21 t^{3}+56 t^{2}-7=0$$

Find the remainder by long division. $$\left(4 s^{3}-9 s^{2}-24 s-17\right) \div(s-5)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$2 x^{3}+11 x^{2}+20 x+12=0 \quad\left(r_{1}=-\frac{3}{2}\right)$$

Solve the given equations without using a calculator. $$2 x^{3}-3 x^{2}-3 x+2=0$$

Find the remainder by long division. $$\left(2 x^{4}-3 x^{3}-2 x^{2}-15 x-16\right) \div(2 x-3)$$

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

Solve the given equations without using a calculator. $$4 x^{3}-16 x^{2}+21 x-9=0$$

Find the remainder by long division. $$\left(2 x^{4}-11 x^{2}-15 x-17\right) \div(2 x+1)$$

Solve the given equations without using a calculator. $$x^{4}-11 x^{2}-12 x+4=0$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(R^{4}+R^{3}-9 R^{2}+3\right) \div(R-3)$$

Solve the given equations without using a calculator. $$8 x^{4}-32 x^{3}-x+4=0$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(4 x^{4}-x^{3}+5 x-7\right) \div(x-5)$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$t^{3}-7 t^{2}+17 t-15=0 \quad\left(r_{1}=2+j\right)$$

Solve the given equations without using a calculator. $$5 n^{4}-2 n^{3}+40 n-16=0$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(2 x^{4}-7 x^{3}-x^{2}+8\right) \div(x+1)$$

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

Solve the given equations without using a calculator. $$8 n^{4}-34 n^{2}+28 n-6=0$$

Find the remainder using the remainder theorem. Do not use synthetic division. $$\left(3 n^{4}-13 n^{2}+10 n-10\right) \div(n+4)$$

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

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. $$4 n^{4}+28 n^{3}+61 n^{2}+42 n+9=0 \quad(-3\text { is a double root) }$$

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. $$6 x^{4}+5 x^{3}-15 x^{2}+4=0 \quad\left(r_{1}=-\frac{1}{2}, r_{2}=\frac{2}{3}\right)$$

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

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

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$6 x^{4}-5 x^{3}-14 x^{2}+14 x-3=0 \quad\left(r_{1}=\frac{1}{3}, r_{2}=\frac{3}{2}\right)$$

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

Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$3 x^{3}+14 x^{2}+7 x-4, x+4$$

Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$3 V^{4}-7 V^{3}+V+8, V-2$$

Solve the given equations without using a calculator. $$2 x^{5}+5 x^{4}-4 x^{3}-19 x^{2}-16 x=4$$

Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$x^{5}-2 x^{4}+3 x^{3}-6 x^{2}-4 x+8, x-1$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$x^{5}-3 x^{4}+4 x^{3}-4 x^{2}+3 x-1=0 \quad(1 \text { is a triple root })$$

Use a calculator to solve the given equations to the nearest 0.01. $$2 x^{3}-8 x+3=0$$

Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$x^{51}-2 x-1, x+1$$

Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$\begin{array}{l}12 x^{5}-7 x^{4}+41 x^{3}-26 x^{2}-28 x+8=0 \\\\\left(r_{1}=1, r_{2}=\frac{1}{4}, r_{3}=-\frac{2}{3}\right) \end{array}$$

Use a calculator to solve the given equations to the nearest 0.01. $$2 x^{4}-15 x^{2}-7 x+3=0$$