Chapter 3

Solve the quadratic inequality. $$x^{2} \leq 4$$

A rational expression is a quotient of two ____.

A rational number is a number that can be expressed as the division of two ________.

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$2 x^{2}+13 x+15 ; x+5$$

Just in Time Exercises These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. A function is symmetric with respect to the _______ if \(f(x)=f(-x)\) for each \(x\) in the domain of \(f .\) Functions having this property are called ______ functions.

Complete them to review topics relevant to the remaining exercises. The __________ of a polynomial is the highest power to which a variable is raised.

Solve the quadratic inequality. $$y^{2} \geq 9$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. The complex conjugate of the number \(a+b i\) is ___________ .

For which values of \(x\) is the following rational expression defined? $$ \frac{x+2}{(x-1)(x+5)} $$

True or False: \(\sqrt{2}\) is a rational number.

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$2 x^{2}-7 x+3 ; x-3$$

Just in Time Exercises These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. A function is symmetric with respect to the _______ if \(f(x)=-f(-x)\) for each \(x\) in the domain of \(f .\) Functions having this property are called ______ functions.

Complete them to review topics relevant to the remaining exercises. What is the degree of the polynomial \(5 x^{4}-2 x-7 ?\).

Solve the quadratic inequality. $$x^{2}+x-6 \leq 0$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Find the conjugate of the complex number \(2+3 i\)

Simplify each rational expression. $$\frac{x^{2}-2 x+1}{2-x-x^{2}}$$

True or False: 0.33333 . . . is a rational number.

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$2 x^{3}-x^{2}-8 x+4 ; 2 x-1$$

Classfy each function as odd, even, or neither. $$f(x)=x^{2}+2$$

Complete them to review topics relevant to the remaining exercises. The __________ of \(f(x)\) are the values of \(x\) such that \(f(x)=0\).

Solve the quadratic inequality. $$x^{2}+x-20 \geq 0$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Find the conjugate of the complex number \(4-i\)

Simplify each rational expression. $$\frac{x^{2}+2 x-15}{x^{2}-9 x+18}$$

True or False: \(-\frac{2}{3}\) is a rational number.

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$3 x^{3}+2 x^{2}-3 x-2 ; 3 x+2$$

Classfy each function as odd, even, or neither. $$h(x)=3|x|$$

Complete them to review topics relevant to the remaining exercises. Find the \(x\) -intercept of \(f(x)=3 x+9\).

Solve the quadratic inequality. $$3 x^{2} \geq 2 x+5$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Find the conjugate of the complex number \(3 i\)

For each polynomial, determine which of the numbers listed next to it are zeros of the polynomial. $$p(x)=(x-10)^{8}, x=6,-10,10$$

Simplify each rational expression. $$\frac{x^{2}-1}{x^{2}-2 x-3}$$

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$x^{3}-3 x^{2}+2 x-4 ; x+2$$

Classfy each function as odd, even, or neither. $$g(x)=-x$$

Complete them to review topics relevant to the remaining exercises. Find the \(y\) -intercept of \(f(x)=3 x+9\).

Solve the quadratic inequality. $$2 x^{2} \leq 3-x$$

These exercises correspond to the Just in Time references in this section. Complete them to review topics relevant to the remaining exercises. Find the conjugate of the complex number \(i \sqrt{7}\)

For each polynomial, determine which of the numbers listed next to it are zeros of the polynomial. $$p(x)=(x+6)^{10}, x=6,-6,0$$

Simplify each rational expression. $$\frac{x+2}{x^{2}+3 x+2}$$

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$x^{3}+2 x^{2}-x-3 ; x-3$$

Classfy each function as odd, even, or neither. $$f(x)=x^{3}$$

Complete them to review topics relevant to the remaining exercises. Multiply: \(x^{3}\left(x^{2}-3\right)(x+1)\).

Solve the polynomial inequality. $$2 x(x+5)(x-3) \geq 0$$

For each polynomial function, list the zeros of the polynomial and state the multiplicity of each zero. $$g(x)=(x-1)^{3}(x-4)^{5}$$

Find the domain and the vertical and horizontal asymptotes (if any). $$h(x)=\frac{-2}{x+6}$$

For each polynomial, determine which of the numbers listed next to it are zeros of the polynomial. $$g(s)=s^{2}+4, s=-2,2$$

Find the quotient and remainder when the first polynomial is divided by the second. You may use synthetic division wherever applicable. $$-3 x^{4}+x^{2}-2 ; 3 x-1$$

Determine the multiplicities of the real zeros of the function. Comment on the behavior of the graph at the \(x\) -intercepts. Does the graph cross or just touch the \(x\) -axis? You may check your results with a graphing utility. $$f(x)=(x-2)^{2}(x+5)^{5}$$

Complete them to review topics relevant to the remaining exercises. Factor: \(x^{3}-3 x^{2}-4 x\)

Solve the polynomial inequality. $$(x+1)^{2}(x-2) \leq 0$$

For each polynomial function, list the zeros of the polynomial and state the multiplicity of each zero. $$f(t)=t^{5}(t-3)^{2}$$