91Ó°ÊÓ

To rationalize the denominator of the expression \(\frac{\sqrt{2}}{1-\sqrt{3}},\) multiply both the numerator and the denominator by which of the following? (a) \(\sqrt{3}\) (b) \(\sqrt{2}\) (c) \(1+\sqrt{3}\) (d) \(1-\sqrt{3}\)

Use synthetic division to find the quotient and remainder when: \(x^{3}+2 x^{2}-3 x+1\) is divided by \(x+1\)

True or False The distance between two distinct points on the real number line is always greater than zero.

Is the expression a monomial? If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not. $$ -4 x^{2} $$

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. \(A \cup B\)

In Problems 13–18, the lengths of the legs of a right triangle are given. Find the hypotenuse. \(a=5, \quad b=12\)

On the real number line, label the points with coordinates \(0,1,-1, \frac{5}{2},-2.5, \frac{3}{4},\) and \(0.25 .\)

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

Use synthetic division to find the quotient and remainder when: \(0.1 x^{3}+0.2 x\) is divided by \(x+1.1\)

Is the expression a monomial? If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not. $$ \frac{8 x}{y} $$