Free Printable Unit 4: Factoring - Study Guide (Grade 11)

1.

Section A — Factor completely: 6x + 3

a)

3(2x + 1)

b)

(x + 3) + 3x

c)

6(x + 1/2)

2.

Section A — Factor completely: $24x^2 - 8x$

a)

8x(3x − 1)

b)

4x(6x − 2)

c)

(12x − 4)x

3.

Section A — Factor completely: $6x - 12$

a)

$6(x - 2)$

b)

(3x - 2)(2x + 2)

c)

6(x - 2)(x + 2)

4.

Section A — Factor completely: $2x^2 + 8x$

a)

2x(x + 4)

b)

(x + 2)(2x + 4)

c)

2(x + 8)

5.

Section A — Factor completely: 4x + 10

a)

2(2x + 5)

b)

(x + 5) + 3x

c)

4(x + 2.5)

6.

Section A — Factor completely: $10x^2 + 35x$

a)

5x(2x + 7)

b)

10x(x + 3.5)

c)

(5x + 7)(2x)

7.

Section A — Factor completely: $10x^2y - 15xy^2$

a)

5xy(2x − 3y)

b)

5xy(2x + 3y)

c)

xy(10x − 15y)

8.

Section A — Factor completely: $12x^2 - 9x + 15$

a)

$3(4x^2 - 3x + 5)$

b)

(3x - 5)(4x - 3)

c)

3(2x - 3)(2x + 5)

9.

Section A — Factor completely: $3n^3 - 12n^2 - 30n$

a)

3n(n − 5)(n + 2)

b)

3n(n − 3)(n − 10)

c)

$n(3n^2 − 12n − 30)$

10.

Section A — Factor completely: $9m^2 - 4m + 12$

a)

Prime (cannot be factored over the integers)

b)

(9m - 4)(m + 3)

c)

(3m - 2)(3m + 6)

11.

Section A — Factor completely: $2x^3 - 3x^2 + 5x$

a)

$x(2x^2 - 3x + 5)$

b)

$(2x - 3)(x^2 + 5)$

c)

x(2x - 5)(x - 1)

12.

Section A — Factor completely: $13m + 26m^2 - 39m^3$

a)

13m(3m + 1)(1 − m)

b)

13m(3m − 1)(m + 1)

c)

13m(m − 3)(m + 1)

13.

Section A — Factor completely: $17x^2 + 34x + 51$

a)

$17(x^2 + 2x + 3)$

b)

(17x + 17)(x + 3)

c)

17(x + 3)(x − 1)

14.

Section A — Factor completely: $18m^2n^4 - 12m^2n^3 + 24m^2n^2$

a)

$6m^2n^2(3n^2 - 2n + 4)$

b)

$6mn(3n^3 - 2n^2 + 4n)$

c)

$12m^2n^2(3n^2 - 2n + 2)$

15.

Section B — Factor completely: $x^2 - 1$

a)

(x − 1)(x + 1)

b)

x(x − 1) + 1

c)

$(x - 1)^2$

16.

Section B — Factor completely: $x^2 - 9$

a)

(x − 3)(x + 3)

b)

(x − 9)(x + 1)

c)

(x − 1)(x + 9)

17.

Section B — Factor completely: $x^2 + 4$

a)

Prime (cannot be factored over the reals)

b)

(x + 2)(x + 2)

c)

(x − 2)(x + 2)

18.

Section B — Factor completely: $x^2 - 25$

a)

(x − 5)(x + 5)

b)

(x − 25)(x + 1)

c)

(x − 1)(x + 25)

19.

Section B — Factor completely: $9y^2 - 16$

a)

(3y − 4)(3y + 4)

b)

(y − 4)(y + 4)

c)

(9y − 16)(y + 1)

20.

Section B — Factor completely: $4x^2 - 25$

a)

(2x - 5)(2x + 5)

b)

(x - 5)(x + 5)

c)

(4x - 25)

21.

Section B — Factor completely: $9x^2 - 1$

a)

(3x − 1)(3x + 1)

b)

(x − 1)(x + 1)

c)

(9x − 1)(x + 1)

22.

Section B — Factor completely: $a^2 - x^2$

a)

(a - x)(a + x)

b)

$(a - x)^2$

c)

$(a + x)^2$

23.

Section B — Factor completely: $25 - m^2$

a)

(5 − m)(5 + m)

b)

(m − 5)(m + 5)

c)

(25 − m)(m + 1)

24.

Section B — Factor completely: $x^2 - 16y^2$

a)

(x - 4y)(x + 4y)

b)

(x - 16y)(x + y)

c)

(x - 8y)(x + 2y)

25.

Section B — Factor completely: $25m^2 - n^2$

a)

(5m - n)(5m + n)

b)

(25m - n)(m + n)

c)

$(5m - n)^2$

26.

Section C — Factor completely: $x^2 + 6x + 8$

a)

(x + 2)(x + 4)

b)

(x + 1)(x + 8)

c)

(x + 3)(x + 3)

27.

Section C — Factor completely: $c^2 + 5c + 6$

a)

(c + 2)(c + 3)

b)

(c + 1)(c + 6)

c)

(c + 5)(c + 1)

28.

Section C — Factor completely: $y^2 - 9y + 14$

a)

(y − 7)(y − 2)

b)

(y − 9)(y + 1)

c)

(y − 6)(y − 3)

29.

Section C — Factor completely: $x^2 - 10x + 16$

a)

(x - 8)(x - 2)

b)

(x - 10)(x + 16)

c)

(x - 4)(x - 4)

30.

Section C — Factor completely: $a^2 + 12a + 27$

a)

(a + 3)(a + 9)

b)

(a + 6)(a + 6)

c)

(a + 1)(a + 27)

31.

Section C — Factor completely: $x^2 - 14x + 24$

a)

(x - 12)(x - 2)

b)

(x - 8)(x - 3)

c)

(x - 6)(x - 4)

32.

Section C — Factor completely: $x^2 - 15x + 36$

a)

(x - 12)(x - 3)

b)

(x - 9)(x - 6)

c)

(x - 18)(x + 3)

33.

Section C — Factor completely: $y^2 + 21y + 54$

a)

(y + 3)(y + 18)

b)

(y + 6)(y + 9)

c)

(y + 27)(y − 2)

34.

Section C — Factor completely: $m^2 + 13m - 36$

a)

prime

b)

(m + 18)(m - 2)

c)

(m + 12)(m + 1)

35.

Section C — Factor completely: $x^2 - 8x + 15$

a)

(x - 5)(x - 3)

b)

(x - 8)(x - 7)

c)

(x - 6)(x - 2)

36.

Section C — Factor completely: $y^2 - 4y - 32$

a)

(y − 8)(y + 4)

b)

(y − 16)(y + 2)

c)

(y − 32)(y + 1)

37.

Section D — Factor completely: $2x^2 - 5x - 3$

a)

(2x + 1)(x - 3)

b)

(2x - 1)(x - 3)

c)

(2x - 3)(x + 1)

38.

Section D — Factor completely: $3x^2 + 10x - 8$

a)

(3x − 2)(x + 4)

b)

(3x + 2)(x − 4)

c)

(3x + 4)(x − 2)

39.

Section D — Factor completely: $2y^2 + 15y + 7$

a)

(2y + 1)(y + 7)

b)

(2y + 7)(y + 1)

c)

(2y − 1)(y + 7)

40.

Section D — Factor completely: $7a^2 - 11a + 4$

a)

(7a - 4)(a - 1)

b)

(7a - 1)(a - 4)

c)

(7a + 4)(a - 1)

41.

Section D — Factor completely: $5n^2 + 17n + 6$

a)

(5n + 2)(n + 3)

b)

(5n + 3)(n + 2)

c)

(5n − 2)(n − 3)

42.

Section D — Factor completely: $4y^2 + 8y + 3$

a)

(2y + 3)(2y + 1)

b)

(4y + 3)(y + 1)

c)

(2y + 1)(2y + 5)

43.

Section D — Factor completely: $3x^2 + 4x - 7$

a)

(3x + 7)(x − 1)

b)

(3x − 7)(x + 1)

c)

(3x + 1)(x − 7)

44.

Section D — Factor completely: $2x^2 + 13x + 15$

a)

(2x + 3)(x + 5)

b)

(2x + 5)(x + 3)

c)

(x + 3)(x + 5)

45.

Section D — Factor completely: $9y^2 + 6y - 8$

a)

(3y + 4)(3y − 2)

b)

(9y − 8)(y + 1)

c)

(3y − 4)(3y + 2)

46.

Section D — Factor completely: $6x^2 - 7x - 20$

a)

(3x + 4)(2x − 5)

b)

(3x − 4)(2x + 5)

c)

(3x + 5)(2x − 4)

47.

Section E — Factor completely: $2x^2 - 8$

a)

2(x − 2)(x + 2)

b)

2x − 8

c)

$2(x^2 - 8)$

48.

Section E — Factor completely: $2x^2 + 8x + 6$

a)

2(x + 1)(x + 3)

b)

(2x + 6)(x + 1)

c)

2(x + 2)(x + 3)

49.

Section E — Factor completely: $3n^2 + 9n - 30$

a)

3(n + 5)(n - 2)

b)

(3n + 9)(n - 10)

c)

3(n - 5)(n + 2)

50.

Section E — Factor completely: $6x^2 - 26x - 20$

a)

2(3x + 2)(x - 5)

b)

2(3x - 2)(x + 5)

c)

(6x + 2)(x - 10)

51.

Section E — Factor completely: $2x^2 + 12x - 80$

a)

2(x + 10)(x − 4)

b)

2(x + 8)(x − 10)

c)

(2x + 12)(x − 80)

52.

Section E — Factor completely: $5t^2 + 15t + 10$

a)

5(t + 1)(t + 2)

b)

(5t + 10)(t + 1)

c)

5(t + 2)(t + 2)

53.

Section E — Factor completely: $8n^2 - 18$

a)

2(2n − 3)(2n + 3)

b)

2(n − 3)(n + 3)

c)

(8n − 18)

54.

Section E — Factor completely: $14x^2 + 7x - 21$

a)

7(2x + 3)(x − 1)

b)

7(2x − 3)(x + 1)

c)

7(2x + 1)(x − 3)

55.

Section F — Factor completely: $x^2 + 2x + xy + 2y$

a)

(x + y)(x + 2)

b)

x(x + y) + 2(x + y)

c)

(x + 2)(x + y) + 0

56.

Section F — Factor completely: $3a^2 - 2b - 6a + ab$

a)

(a − 2)(3a + b)

b)

(3a − 2)(a + b)

c)

(a − b)(3a − 2)

57.

Section F — Factor completely: $t^3-t^2+t-1$

a)

$(t - 1)(t^2 + 1)$

b)

$(t - 1)(t^2 - 1)$

c)

$t^2(t - 1) + (t - 1)$

58.

Section F — Factor completely: 10 + 2t − 5s − st

a)

(t + 5)(2 − s)

b)

(t − 5)(2 + s)

c)

(t + 5)(s − 2)

59.

Section F — Factor completely: (2/3)bc − (14/3)b + c − 7

a)

(c − 7)((2/3)b + 1)

b)

(b − 7)((2/3)c + 1)

c)

(c + 7)((2/3)b − 1)

60.

Section F — Factor completely: $4u^2 + v + 2uv + 2u$

a)

(2u + v)(2u + 1)

b)

(u + v)(4u + 2)

c)

(2u + v)(u + 2)

61.

Section F — Factor completely: $ad + 3a - d^2 - 3d$

a)

(d + 3)(a − d)

b)

(a + d)(d − 3)

c)

(a − 3)(d + d)

62.

Section G — Identify the transformations from the parent function

f(x) = $x^2$ that give g(x) = $−3(x + 4)^2 − 5$

a)

Reflect over the x-axis; vertical stretch by factor 3; translate to left 4; shift down 5

b)

Reflect over the y-axis; vertical stretch by factor 3; translate to right 4; shift up 5

c)

Reflect over the x-axis; vertical compression by factor 1/3; translate to right 4; shift down 5

63.

Section G — Identify the transformations from the parent function f(x) = √x that give g(x) = 1/2 √(−x + 3) + 6

a)

Reflect over the y-axis; shift right 3; vertical compression by factor 1/2; translate to right 5 and up 6

b)

Reflect over the x-axis; shift left 3; vertical stretch by factor 2; translate to left 5 and up 6

c)

No reflection; shift left 3; vertical compression by factor 1/2; translate to right 5 and down 6

64.

Section G — Identify the transformations from the parent function f(x) = |x| that give g(x) = −4|−3x + 9| − 1

a)

vertical stretch by factor 4; horizontal compression of 1/3; reflect over the x-axis and y-axis; translate to right 3 and down 1

b)

vertical stretch by factor 4; reflect over the y-axis; shift right 1 and down 3

c)

vertical compression by factor 1/3; reflect over the x-axis; shift right 3 and up 1

Unit 4: Factoring - Study Guide (Grade 11)

Total questions: 64

Worksheet time: 2hrs 8mins

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