College Algebra Chapter 1 Practice Test

Simplify the following expression. $\frac{-2}{x^2-1}+\frac{1}{x+1}-\frac{1}{x-1}$  

• 0

•  $\frac{-4}{x^2-1}$  

•  $\frac{4}{x^2-1}$  

• 1

• -1

Which of the following expressions is equal to a?

• $\frac{a^4b^{-3}}{a^3b^3}$

• $\frac{a^3b^4}{a^4b^{-4}}$

• $\frac{a^4b^3}{a^3b^3}$

• $\frac{a^3b^{-3}}{a^4b^{-3}}$

• $\frac{a^4b^{-3}}{a^{-3}b^3}$

Which of the following is equal to  $a^{bc}$   for all values of a, b, and c?

•  $ab^c$  

•  $a^{\left(b+c\right)}$  

•  $a^ba^c$  

•  $\left(a^b\right)^c$  

•  $a^bc$  

What are the roots of the following polynomial? $f\left(x\right)=x^3-9x$  

• x=0, 3

• x=-3, 3

• x=-3, 0, 3

• x=-3, 0

• x=3

When expanded, the polynomial $x\left(x-2\right)^2\left(x+4\right)$  is equal to which of the following?

•  $x^4-16x^3+12x$  

•  $x^4-12x^3+16x$  

•  $x^4-12x^2+16x$  

•  $x^4-12x+16$  

•  $x^4-16x^2+12x$  

Which of the following when added to $4a^2+9$  will result in a perfect square for all integer values of a?

• 0

• 3a

• 6a

• 9a

• 12a

Which of the following properties is satisfied by $\sqrt{2}$ ? 
1. Real number
2. Rational number
3. Complex number

• 1 only

• 1 and 2 only

• 1 and 3 only

• 2 and 3 only

• 1,2, and 3

Which of the following is not equivalent to $\frac{\sqrt{8}}{\sqrt{\sqrt{32}}}$  ?

•  $\frac{1}{2}$  

•  $2^{\frac{1}{4}}$  

•  $\frac{\sqrt{2}}{\sqrt{\sqrt{2}}}$  

•  $\frac{2^{\frac{1}{2}}}{2^{\frac{1}{4}}}$  

 $a\left(x+b\right)=4x+10$  
In the equation above, a and b are constants. If the equation has infinitely many solutions for x, what is the value of b?

• 2

• 3

• 4

• 5

• 10

 Which is equivalent to $\sqrt{18}-4\sqrt{8}+2\sqrt{50}$ ?

•  $-5\sqrt{2}$  

•  $5\sqrt{2}$  

•  $3\sqrt{2}$  

• 0

•  $-\sqrt{60}$