# Sample quiz on factoring quadratics Main home here.

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 $x^2-49x+600$.
$(x-20)(x-30)$
$(x+20)(x+30)$
$(x+24)(x+25)$
$(x-24)(x-25)$