91Ó°ÊÓ

Replace the question mark by \(<,>,\) or \(=\), whichever is correct. \(5 ? 6\)

Factor each polynomial by factoring out the common monomial factor. $$ 3 x^{2} y-6 x y^{2}+12 x y $$

Perform the indicated operation and simplify the result. Leave your answer in factored form. $$ \frac{3}{2 x} \cdot \frac{x^{2}}{6 x+10} $$

Use \(U=\) universal set \(=\\{0,1,2,3,4,5,6,7,8,9\\}, A=\\{1,3,4,5,9\\}, B=\\{2,4,6,7,8\\},\) and \(C=\\{1,3,4,6\\}\) to find each set. $$ \overline{B \cup C} $$

Use \(U=\) universal set \(=\\{0,1,2,3,4,5,6,7,8,9\\}, A=\\{1,3,4,5,9\\}, B=\\{2,4,6,7,8\\},\) and \(C=\\{1,3,4,6\\}\) to find each set. $$ \bar{B} \cap \bar{C} $$

Use synthetic division to determine whether \(x-\) c is a factor of the given polynomial. \(4 x^{4}-15 x^{2}-4 ; \quad x-2\)

Is the expression a polynomial? If it is, give its degree. If it is not, state why not. $$ -\pi $$

List the numbers in each set that are (a) Natural numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers. $$E=\left\\{\sqrt{2}, \pi, \sqrt{2}+1, \pi+\frac{1}{2}\right\\}$$

Find the area \(A\) of a rectangle with length 9 centimeters and width 4 centimeters.

Challenge Problem Use synthetic division to divide $$ x^{4}+(3-h) x^{3}-2 h x^{2}-2 h^{2} x+h^{3} \text { by } x-h $$