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Magazine Problem 18
Solve the given equations without using a calculator. $$x^{6}-x^{4}-14 x^{2}+24=0$$
Problem 18
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$3 x^{3}+14 x^{2}+7 x-4, x+4$$
Problem 19
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$3 V^{4}-7 V^{3}+V+8, V-2$$
Problem 20
Solve the given equations without using a calculator. $$2 x^{5}+5 x^{4}-4 x^{3}-19 x^{2}-16 x=4$$
Problem 20
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$x^{5}-2 x^{4}+3 x^{3}-6 x^{2}-4 x+8, x-1$$
Problem 21
Use a calculator to solve the given equations to the nearest 0.01. $$2 x^{3}-8 x+3=0$$
Problem 21
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$x^{51}-2 x-1, x+1$$
Problem 21
Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$x^{5}-3 x^{4}+4 x^{3}-4 x^{2}+3 x-1=0 \quad(1 \text { is a triple root })$$
Problem 22
Find the remaining roots of the given equations using synthetic division, given the roots indicated. $$\begin{array}{l}12 x^{5}-7 x^{4}+41 x^{3}-26 x^{2}-28 x+8=0 \\\\\left(r_{1}=1, r_{2}=\frac{1}{4}, r_{3}=-\frac{2}{3}\right) \end{array}$$
Problem 22
Use the factor theorem to determine whether or not the second expression is a factor of the first expression. Do not use synthetic division. $$x^{7}-128^{-1}, x+2^{-1}$$
