Free Printable Factoring Quadratic (With a Some Solving)

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Factoring Quadratic (With a Some Solving)

Total questions: 60

Worksheet time: 5hrs 0mins

Name

Class

Date

Solve by finding the solution.
(x+4) (x-3) = 0

x = -4
x = 3

x = 4
x = 3

x = 3/4
x = 1

x = 7
x = 0

Find the solution.
7x (x - 6) = 0

x = -6
x = 0

x = 0
x = 1

x = 6
x = 0

x = 7
x = 6

Find the solution.
(x - 11) (5x - 1) = 0

x = 1
x = 11

x = 11
x = 1/5

x = 5
x = 0

x = 5
x = 11

Find the solution.
(3x + 1) (x - 1) = 0

x = 1
x = 3

x = 1
x = - 1/3

x = 3
x = - 1

x = 4
x = -1

Factor and find the solution

p² - 49

p = 49

p = - 49

p = 2

p = 17

p = 49

p = -7

p = 7

Factor and find the solution

m² - 121 = 0

m = 121

m = - 121

m = - 11

m = 11

m = 121

m = 1

m = 121

Completely factor the following expression.

16a² - 8a

8a (2a - 1)

16 ( a² - 8a)

a (16a - 8)

2a (8a- 4)

Completely factor the following expression.

15h² + 20h

5h (3h + 4)

15h (h + 5)

3h (5h + 7)

35h²

Completely factor the following expression.

15h² + 20h

5h (3h + 4)

15h (h + 5)

3h (5h + 7)

35h²

10.

Completely factor the following expression.

21x²+ 20x

20x (x + 1)

2x ( 10x +3)

x (21x + 20)

20x

11.

Which is not a factor of

12x^2-2x-24

$4x+3$

$3x+4$

$2x-3$

$2$

12.

Convert x²-9x+20 to factored form.

(x-10) (x+2)

(x+4) (x+5)

(x-4) (x-5)

Not factorable

13.

y = 2x² - x - 3 factors into

(2x+3)(x-1)

(2x-3)(x-1)

(2x-3)(x+1)

(2x+3)(x+1)

14.

Factor: x² + 2x – 3

(x - 2)(x + 1)

(x + 1)(x - 3)

(x + 2)(x - 1)

(x - 1)(x + 3)

15.

Solve by factoring:

$3x^2-11x+6=0$

$\left(3x-2\right)\ and\ \left(x-3\right)$

$\left(3x\ +\ 2\right)\ and\ \left(x\ +3\right)$

$\left(-2x\ +3\right)\ and\ \ \left(3x\ +1\right)$

$\left(x\ +\ 3\right)\ \left(x\ -6\right)$

16.

Factor:

(x + 3)(x + 10)

(x - 3)(x - 10)

(x + 3)(x - 10)

(x - 3)(x + 10)

17.

Factor:

(x + 2)(x + 2) = (x + 2)²

(x - 2)(x - 2) = (x - 2)²

(x + 2)(x - 2)

(x - 2)(x + 2)

18.

Factor:

(x + 6)(x + 8)

(x - 6)(x - 8)

(x + 6)(x - 8)

(x - 6)(x + 8)

19.

Factor:

(x + 6)(x + 4)

(x - 6)(x - 4)

(x + 6)(x - 4)

(x - 6)(x + 4)

20.

Factor:

(x + 2)(x + 5)

(x - 2)(x - 5)

(x + 2)(x - 5)

(x - 2)(x + 5)

21.

Factor:

(x + 4)(x + 7)

(x - 4)(x - 7)

(x + 4)(x - 7)

(x - 4)(x + 7)

22.

Factor:

(x + 6)(x + 8)

(x - 6)(x - 8)

(x + 6)(x - 8)

(x - 6)(x + 8)

23.

Factor:

(x + 1)(x + 10)

(x - 1)(x - 10)

(x + 1)(x - 10)

(x - 1)(x + 10)

24.

Factor:

(x + 9)(x + 2)

(x - 9)(x - 2)

(x + 9)(x - 2)

(x - 9)(x + 2)

25.

Factor:

(x + 8)(x + 5)

(x - 8)(x - 5)

(x + 8)(x - 5)

(x - 8)(x + 5)

26.

Factor:

(x + 7)(x + 5)

(x - 7)(x - 5)

(x + 7)(x - 5)

(x - 7)(x + 5)

27.

Factor:

(x + 3)(x + 6)

(x - 3)(x - 6)

(x + 3)(x - 6)

(x - 3)(x + 6)

28.

Factor:

(x + 3)(x + 5)

(x - 3)(x - 5)

(x + 3)(x - 5)

(x - 3)(x + 5)

29.

Factor:

(x + 8)(x + 10)

(x - 8)(x - 10)

(x + 8)(x - 10)

(x - 8)(x + 10)

30.

Factor:

(x + 7)(x + 2)

(x - 7)(x - 2)

(x + 7)(x - 2)

(x - 7)(x + 2)

31.

Factor:

(x + 4)(x + 5)

(x - 4)(x - 5)

(x + 4)(x - 5)

(x - 4)(x + 5)

32.

Factor:

(x + 1)(x + 1) = (x + 1)²

(x - 1)(x - 1) = (x - 1)²

(x + 1)(x - 1)

(x - 1)(x + 1)

33.

Factor:

(x + 10)(x + 2)

(x - 10)(x - 2)

(x + 10)(x - 2)

(x - 10)(x + 2)

34.

Factor:

(x + 9)(x + 6)

(x - 9)(x - 6)

(x + 9)(x - 6)

(x - 9)(x + 6)

35.

Factor:

(x + 3)(x + 1)

(x - 3)(x - 1)

(x + 3)(x - 1)

(x - 3)(x + 1)

36.

2x + 4

2(x + 2)

2(x + 4)

4(x + 4)

4(x + 2)

37.

5x² + 20

5(x + 4)

5x(x + 4)

5(x² + 4)

5x²(x + 4)

38.

x⁵ + x⁴ + x²

x³(x² + x + 1)

x(x⁴ + x³ + x)

x²(x³ + x²)

x²(x³ + x² + 1)

39.

15x⁴ + 20x³ - 25x

5x²(3x² + 4x - 5)

5x(3x³ + 4x² - 5x)

5x(3x³ + 4x² - 5)

5(3x⁴ + 4x³ - 5x)

40.

Find the GCF of 64 and 144

41.

What is the GCF of the trinomial?
3x²- 9x -120

42.

Factor:
2n²-8n³

2n²(n-4n²)

2n²(1-4n)

2n³(10-8n²)

3n(1-4n)

43.

Factor by GCF:

17xy - x

17(xy - x)

y(17x - x)

x(17y - 1)

Prime

44.

Factor using the GCF method
10x + 15

100x + 150

10(x + 5)

1(10x + 15)

5(2x + 3)

45.

Factor using the GCF method
8r³ + 16r²

4r²(2r + 4)

8r²(r + 2)

8(r³ + r²)

4(r³ + 2r²)

46.

Factor Completely
5x³-7x²

x²(5x-7)

x(5x²-7x)

x³(5-7x)

Prime

47.

What is the GCF? 5x²+20x

20x

48.

Which of the following is a factor of:
4x²+44x-104

(x-4)

(x+2)

(x+13)

(x+11)

49.

Factor:
16x² + 18x + 12

4(4x² + 6x + 3)

2(8x² + 9x + 6)

2x(8x + 9 + 3)

x(16x + 18 + 12)

50.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

3(x² + 6x + 5)

(x + 5)(x + 1)

3(x + 5)(x + 1)

Prime

51.

Factor completely:
3x² + 18x +15
Hint: Factor GCF first.

3(x² + 6x + 5)

(x + 5)(x + 1)

3(x + 5)(x + 1)

Prime

52.

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

length = 26 yd, width = 21 yd

length = 21 yd, width = 26 yd

length = 21 yd, width = 16 yd

length = 16 yd, width = 21 yd

53.

Suppose that the equation V = 20.8x² – 458.3x + 3,500 represents the value of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964)

1965

1970

1975

1980

54.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation s(t) = –16t² + 64t + 80. What will be the object's maximum height?

2 ft

80 ft

144 ft

64 ft

55.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t) = -16t² +128t (if air resistance is neglected). When will the object reach its maximum height?

4 ft

0 seconds

0 ft

4 seconds

56.

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

4 seconds

-2 seconds

-6 seconds

9 seconds

57.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket. What is the maximum profit you can make from selling tickets?

$6060

$20

$600

$10,250

58.

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation

h = -2t²+ 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

59.

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t²+ 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

0.5 seconds

1 second

1.5 seconds

2 seconds

3 seconds

60.

Leslie Knope is planning on building a park. She knows the area of the park can be calculated from using the equation p(x) = 5x² + 17x + 6. Ron Swanson wrote the dimensions of the park in factored form. Which of the following could be the possible dimensions of the park.

Length = (x + 6)

Width = (5x +17)

Length = (5x + 2)

Width = (x + 3)

Length = (2x + 5)

Width = (3x + 1)

Length = (x + 5)

Width = (x + 6)

100 %

Factoring Quadratic (With a Some Solving)

Total questions: 60

Worksheet time: 5hrs 0mins

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