Grade 10 Practice Factoring and Quadratic Equations
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Expand and simplify (2x - 1)(x + 3)
a.
b.
c.
d.
2. Factor completely:
a.
b.
c.
d.
3. Factor completely:
a.
b.
c.
d.
4. Factor completely:
a.
b.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
c.
d.
____ 15. Expand and simplify 3x(x - 2)
a.
b.
c.
d.
____ 16. Factor completely:
a.
b.
c.
d.
____ 17. Factor completely:
a.
b.
c.
d.
____ 18. Factor completely:
a.
b.
c.
d.
____
____
____
____
____
____
____
5. Factor completely:
a.
b.
6. Expand and simplify -3x(2x - 1)
a.
b.
7. Expand and simplify (2x - 1)(x - 3)
a.
b.
8. Factor completely:
a.
b.
____
9. Factor completely:
a.
b.
____ 10. Expand and simplify -2x(x - 3)
a.
b.
____ 11. Factor completely:
a.
b.
____ 12. Factor completely:
a.
b.
____ 13. Expand and simplify (2x + 3)(x - 1)
a.
b.
____ 14. Factor completely:
a.
b.
____ 19. Factor completely:
a.
b.
c.
d.
____ 20. Factor completely:
a.
b.
c.
d.
____ 21. Factor completely:
a.
b.
c.
d.
____ 22. Factor completely:
a.
b.
c.
d.
c.
d.
____ 23. Factor completely:
a.
b.
____ 24. Write an equation that has roots -1 and 2.
a.
b.
____ 25. The following diagram illustrates that
a.
b.
c.
d.
c.
d.
____ 26. Factor completely:
a.
b.
c.
d.
____ 27. Factor completely:
a.
b.
c.
d.
____ 28. Factor completely:
a.
b.
c.
d.
____ 29. Factor completely:
a.
b.
c.
d.
____ 30. Factor completely:
a.
b.
c.
d.
____ 31. Expand and simplify 2x(3x - 1)
a.
b.
c.
d.
____ 32. Expand and simplify (2x + 1)(x - 3)
a.
b.
c.
d.
____ 33. Factor completely:
a.
____ 34. Factor completely:
a.
b.
c.
d.
b.
c.
d.
c.
d.
____ 35. Factor completely:
a.
b.
____ 36. The following diagram illustrates that
a.
b.
c.
d.
____ 37. Solve for x:
a.
or
b.
____ 38. Solve for x:
a.
or
b.
____ 39. Factor completely:
a.
b.
c.
d.
____ 40. Factor completely:
a.
b.
c.
d.
____ 41. Factor completely:
a.
b.
c.
d.
____ 42. Factor completely:
a.
b.
c.
d.
c.
d.
or
or
____ 43. Factor completely:
a.
b.
____ 44. The following diagram illustrates that
c.
or
d.
or
c.
or
d.
or
a.
b.
c.
d.
____ 45. Write the equation of a parabola that has zeros at -1 and 2.
a.
c.
b.
d.
____ 46. Write an equation that has roots -2 and 1.
a.
c.
b.
d.
____ 47. Factor completely:
a.
b.
____ 48. The following diagram illustrates that
a.
b.
c.
d.
c.
d.
____ 49. Write the equation of a parabola that has zeros at -2 and 1.
a.
c.
b.
d.
____ 50. Solve for x:
a.
b.
c.
or
or
or
d.
or
____ 51. Solve for x:
a.
or
d.
or
b.
or
c.
or
Grade 10 Practice Factoring and Quadratic Equations
Answer Section
MULTIPLE CHOICE
1. ANS: B
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x .)
or...
PTS: 1
2. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
3. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
4. ANS: A
Arrange the tiles into a rectangle:
So
PTS: 1
5. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
6. ANS: A
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that -3x multiplied by 2x is -6x .)
or...
PTS: 1
7. ANS: B
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x .)
or...
PTS: 1
8. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
9. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
10. ANS: D
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x .)
or...
PTS: 1
11. ANS: A
Arrange the tiles into a rectangle:
So
PTS: 1
12. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
13. ANS: C
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x .)
or...
PTS: 1
14. ANS: C
The expression has a common factor of 3x. 3x must multiply by x and by -1 to give
.
PTS: 1
15. ANS: C
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 3x multiplied by x is 3x .)
or...
PTS: 1
16. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
17. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
18. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
19. ANS: D
The expression has a common factor of -2x. -2x must multiply by x and by -3 to give
PTS: 1
20. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
21. ANS: A
Arrange the tiles into a rectangle:
.
So
PTS: 1
22. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
23. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
24. ANS: B
The equation is
(NOT roots) at -1 and 2.
. Note that
is the equation of a parabola that has zeros
PTS: 1
25. ANS: D
The two expressions that are multiplied are -2x-1 and 3x-4, and the product is
simplifies to
which
PTS: 1
26. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
27. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
28. ANS: C
The expression has a common factor of 3x. 3x must multiply by 3x and by -2 to give
PTS: 1
29. ANS: A
Arrange the tiles into a rectangle:
.
So
PTS: 1
30. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
31. ANS: A
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 3x multiplied by x is 3x .)
or...
PTS: 1
32. ANS: C
We can think of this multiplication using tiles ... but it is not necessary to draw the tiles every time. The
following diagram illustrates the multiplication (as long as you understand that 2x multiplied by x is 2x .)
or...
PTS: 1
33. ANS: A
Arrange the tiles into a rectangle:
So
= (x+2)(2x+1).
PTS: 1
34. ANS: D
Arrange the tiles into a rectangle:
So
PTS: 1
35. ANS: B
Arrange the tiles into a rectangle:
So
PTS: 1
36. ANS: C
The two expressions that are multiplied are 2x-1 and 3x-4, and the product is
simplifies to
which
PTS: 1
37. ANS: D
If
then
or
, so
PTS: 1
38. ANS: A
If
then
or
, so
PTS: 1
39. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
40. ANS: C
Arrange the tiles into a rectangle:
So
PTS: 1
41. ANS: A
Arrange the tiles into a rectangle:
or
or
So
PTS: 1
42. ANS: C
The expression has a common factor of x. x must multiply by 2x and by -1 to give
.
PTS: 1
43. ANS: A
Arrange the tiles into a rectangle:
So
PTS: 1
44. ANS: B
The two expressions that are multiplied are 2x-1 and 3x+4, and the product is
simplifies to
PTS: 1
45. ANS: D
The equation is
PTS: 1
46. ANS: B
The equation is
roots) at -2 and 1.
. Note that
. Note that
PTS: 1
47. ANS: B
Arrange the tiles into a rectangle:
which
is an equation that has roots at -1 and 2.
is the equation of a parabola that has zeros (NOT
So
PTS: 1
48. ANS: D
The two expressions that are multiplied are -2x-1 and -3x+4, and the product is
simplifies to
PTS: 1
49. ANS: D
The equation is
. Note that
is an equation that has roots at -2 and 1.
PTS: 1
50. ANS: C
If
then
or
, so
PTS: 1
51. ANS: B
If
then
or
, so
PTS: 1
which
or
or