Sample quiz on factoring quadratics
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1. Factor $x^2+3x+2$.
   
   $(x+1)(x-2)$
   $(x+1)(x+2)$
   $(x+2)(x+3)$
   $(x-1)(x-2)$
   
2. Factor $x^2+x+2$
   
   $(x+1)(x+2)$
   $(x+1)(x-2)$
   $(x^2+1)(x+2)$
   Not factorable
3. Which of the following quadratics does not factor over the real numbers?
   
   $x^2-2x+1$
   $x^2+3x-4$
   $x^2-5x+6$
   $x^2+2x+8$
4. Factor $x^2-3x-4$.
   
   $(x+1)(x+4)$
   $(x+1)(x-4)$
   $(x+2)(x-4)$
   $(x-2)(x+4)$
5. Factor $2x^2+10x-12$.
   
   $2(x+1)(x+6)$
   $2(x+1)(x-6)$
   $2(x-1)(x+6)$
   $2(x-1)(x+12)$
6. Factor $3x^2-3x-6$
   
   $3(x+1)(x-2)$
   $3(x+1)(x-3)$
   $3(x-1)(x+2)$
   $3(x+1)(x+3)$
7. Factor $3x^2+10x+3$
   
   $3(x+1)(x+3)$
   $(3x+1)(3x+3)$
   $(3x+1)(x+3)$
   Not factorable
8. Factor $2x^2+5x+2$
   
   $(x+2)(2x-1)$
   $(x+2)(2x+2)$
   $(x-2)(2x+1)$
   $(x+2)(2x+1)$
9. Factor $2x^2+7x+3$
   
   $(2x+1)(x+3)$
   $(x+2)(2x+3)$
   $(3x+1)(x+2)$
   $(2x-1)(x-3)$
10. Factor $x^2+8x+15$.
    
    $(x+3)(x+8)$
    $(x+5)(x+3)$
    $(x+5)(x-3)$
    $(x+8)(x+3)$
11. For which of the following values of $b$ is the quadratic $x^2+bx+3$ factorable over the integers?
    
    $b=1$
    $b=2$
    $b=3$
    $b=4$
12. For which of the following values of $b$ is the quadratic $3x^2+bx+5$ factorable over the integers?
    
    $b=3$
    $b=5$
    $b=8$
    $b=15$
13. Given a general quadratic $ax^2+bx+c$, under which condition does it factor over the rational numbers?
    
    when $b^2-4ac$ is equal to zero
    when $b^2-4ac$ is a positive number
    when $b^2+4ac$ is a perfect square
    when $b^2-4ac$ is a perfect square
14. Under what condition does a general quadratic $ax^2+bx+c$ factor as a perfect square?
    
    if $b^2-4ac=1$
    if $b^2-4ac=0$
    if $b^2+4ac=0$
    if $b^2-4ac\geq 0$
15. Factor $2x^2-18$.
    
    $2(x+3)(x-6)$
    $2(x+3)(x-3)$
    $(2x+3)(x-6)$
    $2(x+9)(x-9)$
16. Factor $5x^2+20$.
    
    Not factorable
    $5(x+2)(x+2)$
    $5(x+2)(x-2)$
    $5(x+1)(x+20)$
17. Which of the following quadratics factors as a perfect square?
    
    $x^2+2x+2$
    $x^2+4x+4$
    $x^2+6x+6$
    $x^2+8x+8$
18. For which of the following values of $c$ does the quadratic $x^2+2x+c$ factor over the integers?
    
    $c=-3$
    $c=-2$
    $c=-1$
    None of the above
19. For what value(s) of $b$ does the quadratic $x^2+bx+16$ factor as a perfect square trinomial?
    
    $b=\pm 4$
    $b=\pm 6$
    $b=\pm 8$
    $b=-8$
20. Factor $x^2-49x+600$.
    
    $(x-20)(x-30)$
    $(x+20)(x+30)$
    $(x+24)(x+25)$
    $(x-24)(x-25)$