Kuta Software – Infinite Algebra 1Name___________________________________

Solving Quadratic Equations by Factoring

Date________________ Period____

Solve each equation by factoring.

1) (k + 1)(k − 5) = 0

2) (a + 1)(a + 2) = 0

3) (4k + 5)(k + 1) = 0

4) (2m + 3)(4m + 3) = 0

5) x 2 − 11 x + 19 = −5

6) n 2 + 7n + 15 = 5

7) n 2 − 10n + 22 = −2

8) n 2 + 3n − 12 = 6

9) 6n 2 − 18n − 18 = 6

10) 7r 2 − 14r = −7

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Worksheet by Kuta Software LLC

11) n 2 + 8n = −15

12) 5r 2 − 44r + 120 = −30 + 11r

13) −4k 2 − 8k − 3 = −3 − 5k 2

14) b 2 + 5b − 35 = 3b

15) 3r 2 − 16r − 7 = 5

16) 6b 2 − 13b + 3 = −3

17) 7k 2 − 6k + 3 = 3

18) 35k 2 − 22k + 7 = 4

19) 7 x 2 + 2 x = 0

20) 10b 2 = 27b − 18

21) 8 x 2 + 21 = −59 x

22) 15a 2 − 3a = 3 − 7a

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Worksheet by Kuta Software LLC

Kuta Software – Infinite Algebra 1

Name___________________________________

Solving Quadratic Equations by Factoring

Date________________ Period____

Solve each equation by factoring.

1) (k + 1)(k − 5) = 0

2) (a + 1)(a + 2) = 0

{−1, 5}

{−1, −2}

3) (4k + 5)(k + 1) = 0

{

5

− , −1

4

4) (2m + 3)(4m + 3) = 0

}

5) x 2 − 11 x + 19 = −5

{

3 3

− ,−

2 4

6) n 2 + 7n + 15 = 5

{3, 8}

7) n 2 − 10n + 22 = −2

{−5, −2}

8) n 2 + 3n − 12 = 6

{6, 4}

9) 6n 2 − 18n − 18 = 6

{3, −6}

10) 7r 2 − 14r = −7

{1 }

{4, −1}

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}

-1-

Worksheet by Kuta Software LLC

11) n 2 + 8n = −15

12) 5r 2 − 44r + 120 = −30 + 11r

{−5, −3}

{6, 5}

13) −4k 2 − 8k − 3 = −3 − 5k 2

14) b 2 + 5b − 35 = 3b

{8, 0}

{−7, 5}

15) 3r 2 − 16r − 7 = 5

16) 6b 2 − 13b + 3 = −3

{ }

{ }

2

− ,6

3

2 3

,

3 2

17) 7k 2 − 6k + 3 = 3

18) 35k 2 − 22k + 7 = 4

{ }

{ }

6

,0

7

1 3

,

5 7

19) 7 x 2 + 2 x = 0

20) 10b 2 = 27b − 18

{ }

{ }

2

− ,0

7

6 3

,

5 2

21) 8 x 2 + 21 = −59 x

{

3

− , −7

8

22) 15a 2 − 3a = 3 − 7a

{ }

1 3

,−

3 5

}

Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com

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Worksheet by Kuta Software LLC

Kuta Software – Infinite Algebra 1

Name___________________________________

Using the Quadratic Formula

Date________________ Period____

Solve each equation with the quadratic formula.

1) m 2 − 5m − 14 = 0

2) b 2 − 4b + 4 = 0

3) 2m 2 + 2m − 12 = 0

4) 2 x 2 − 3 x − 5 = 0

5) x 2 + 4 x + 3 = 0

6) 2 x 2 + 3 x − 20 = 0

7) 4b 2 + 8b + 7 = 4

8) 2m 2 − 7m − 13 = −10

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Worksheet by Kuta Software LLC

9) 2 x 2 − 3 x − 15 = 5

10) x 2 + 2 x − 1 = 2

11) 2k 2 + 9k = −7

12) 5r 2 = 80

13) 2 x 2 − 36 = x

14) 5 x 2 + 9 x = −4

15) k 2 − 31 − 2k = −6 − 3k 2 − 2k

16) 9n 2 = 4 + 7n

17) 8n 2 + 4n − 16 = −n 2

18) 8n 2 + 7n − 15 = −7

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-2-

Worksheet by Kuta Software LLC

Kuta Software – Infinite Algebra 1

Name___________________________________

Using the Quadratic Formula

Date________________ Period____

Solve each equation with the quadratic formula.

1) m 2 − 5m − 14 = 0

2) b 2 − 4b + 4 = 0

{2 }

{7, −2}

3) 2m 2 + 2m − 12 = 0

4) 2 x 2 − 3 x − 5 = 0

{2, −3}

{ }

5

, −1

2

5) x 2 + 4 x + 3 = 0

6) 2 x 2 + 3 x − 20 = 0

{−1, −3}

{ }

5

, −4

2

7) 4b 2 + 8b + 7 = 4

{

1 3

− ,−

2 2

8) 2m 2 − 7m − 13 = −10

{

}

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-1-

7+

4

73 7 −

,

73

4

}

Worksheet by Kuta Software LLC

9) 2 x 2 − 3 x − 15 = 5

10) x 2 + 2 x − 1 = 2

{1, −3}

{ }

4, −

5

2

11) 2k 2 + 9k = −7

{

−1, −

7

2

12) 5r 2 = 80

{4, −4}

}

13) 2 x 2 − 36 = x

14) 5 x 2 + 9 x = −4

{ }

{

4

− , −1

5

9

, −4

2

15) k 2 − 31 − 2k = −6 − 3k 2 − 2k

16) 9n 2 = 4 + 7n

{

{ }

5 5

,−

2 2

17) 8n 2 + 4n − 16 = −n 2

{

−2 + 2 37 −2 − 2 37

,

9

9

}

7+

193 7 − 193

,

18

18

}

18) 8n 2 + 7n − 15 = −7

}

{

−7 + 305 −7 − 305

,

16

16

}

Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com

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Worksheet by Kuta Software LLC

CORNELL NOTES

SHEET

QUESTIONS

Name:

Class: MAC1105 Topic: ______Quadratic Notes __________________

Date: 02_____/ __28___/ ____2022____

Period Spring Semester ______

NOTES

SUMMARY: Write 4 or more sentences describing specific learning from these notes.

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

CORNELL NOTES

SHEET

QUESTIONS

Name: ________John Doe_________________________

Class: ___MAC1105___________ Topic: _Complex Numbers___

Date: ____01___/ _04___/ __2022____

Period _Spring 2022___

NOTES

The imaginary unit is denoted by the letter “i”, and i = sqrt (-1)

Addition: (3 + 3i) + (2 – i) = 3 + 3i + 2 – i = 5 – 2i

Subtraction: (4 + 3i) – (-2 – 5i) = 4 + 3i + 2 + 5i = 6 + 8i

Why were called imaginary?

Multiplication: 4( 3 + 2i) = 4(3) + 4(2i) = 12 + 8i

Who introduced the complex

numbers in Math?

Complex conjugate of a + bi is a – bi

Division: 3/(2 + i) = 3(2 -i)/(2+i)(2-i) = (6 – 3i)/ (4 +1) = (6 – 3i)/5 =

= 6/5 – 3i/5

How are complex numbers

used in real life?

Powers of i: i^ 21. Divide 21 by 4, the remainder 1 is the new exponent, so

I^21 = i^1 = i

SUMMARY: Write 4 or more sentences describing specific learning from these notes.

__________________________________________________________________________________________

__I learned what a complex number is; the different operations that we can perform: addition, subtraction, _

__multiplication, division, and powers of i. _______________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Test Content

Question 1

Solve the equation by factoring.

12×2 + 23x + 10 = 0

Question 2

Solve the equation by factoring.

7 – 7x = (4x + 9)(x – 1)

{-4, 1}

{-1, 4}

Question 3

Solve the equation by factoring.

4×2 – 7x = 2

{-4, 2}

Question 4

Solve the equation by factoring.

2×2 – 15x = 8

{-2, 8}

Question 5

Solve the equation by factoring.

2x(x – 5) = 6×2 – 11x

{0}

{0, 4}

Question 6

Perform the indicated operations and write the result in standard form.

Question 7

Perform the indicated operations and write the result in standard form.

-6

6

6i2

-6i

Question 8

Perform the indicated operations and write the result in standard form.

32i

-12i

-12

12i

Question 9

Perform the indicated operations and write the result in standard form.

Question 10

Perform the indicated operations and write the result in standard form.

Question 11

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm’s law relates

the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the

circuit, R, in ohms, by the formula Solve the problem using this formula.

Find E, the voltage of a circuit, if I = (2 + 5i) amperes and R = (8 + 2i) ohms.

(44 – 6i) volts

(6 – 44i) volts

(44 + 6i) volts

(6 + 44i) volts

Question 12

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm’s law relates

the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the

circuit, R, in ohms, by the formula Solve the problem using this formula.

Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.

(28 + 66i) volts

(-32 – 66i) volts

(-32 + 66i) volts

(28 – 66i) volts

Question 13

Perform the indicated operations and write the result in standard form.

(3 + i)2 – (2 – i)2

-5 + 10i

5 – 10i

5 + 10i

-5

Question 14

Perform the indicated operations and write the result in standard form.

(3 + i)2 – (2 – i)2

5 + 10i

-5

-5 + 10i

5 – 10i

Question 15

Find the product and write the result in standard form.

(7 + 3i)(7 – 3i)

49 – 9i2

58

40

49 – 9i

Question 16

Compute the discriminant. Then determine the number and type of solutions for the given equation.

6×2 = -8x – 7

232; two unequal real solutions

0; one real solution

-104; two complex imaginary solutions

Question 17

Compute the discriminant. Then determine the number and type of solutions for the given equation.

x2 + 4x + 3 = 0

4; two unequal real solutions

0; one real solution

-28; two complex imaginary solutions

Question 18

Compute the discriminant. Then determine the number and type of solutions for the given equation.

x2 + 7x + 6 = 0

-73; two complex imaginary solutions

0; one real solution

25; two unequal real solutions

Question 19

Solve the equation by completing the square.

x2 – 12x – 11 = 0

Question 20

Determine the constant that should be added to the binomial so that it becomes a perfect square

trinomial. Then write and factor the trinomial.

x2 – 8x

64; x2 – 8x + 64 = (x – 8) 2

-64; x2 – 8x – 64 = (x – 8) 2

16; x2 – 8x + 16 = (x – 4) 2

-16; x2 – 8x – 16 = (x – 4) 2

Question 21

Determine the constant that should be added to the binomial so that it becomes a perfect square

trinomial. Then write and factor the trinomial.

x2 – 18x

324; x2 – 18x + 324 = (x – 18) 2

-81; x2 – 18x – 81 = (x – 9) 2

81; x2 – 18x + 81 = (x – 9) 2

-324; x2 – 18x – 324 = (x – 18) 2

Question 22

Solve the equation by completing the square.

x2 – 6x + 34 = 0

{3 ± 25i}

{3 + 5i}

{8, -2}

{3 ± 5i}

Question 23

Determine the constant that should be added to the binomial so that it becomes a perfect square

trinomial. Then write and factor the trinomial.

x2 – 13x

Question 24

Solve the equation by completing the square.

16×2 – 5x + 1 = 0

Question 25

Solve the equation by completing the square.

x2 + 4x – 9 = 0

Question 26

Divide and express the result in standard form.

-i

– +i

-i

– -i

Question 27

Divide and express the result in standard form.

+i

-i

-i

+i

Question 28

Divide and express the result in standard form.

1 + 2i

1 + 5i

1 – 2i

-1 + 2i

Question 29

Divide and express the result in standard form.

-i

-i

-i

-i

Question 30

Divide and express the result in standard form.

-1

i

-i

1

Question 31

Solve the equation using the quadratic formula.

3×2 + 10x + 6 = 0

Question 32

Solve the equation using the quadratic formula.

9×2 + 7x + 3 = 0

Question 33

Solve the equation using the quadratic formula.

5×2 + x – 2 = 0

Question 34

Solve the equation using the quadratic formula.

4×2 + 5x + 7 = 0

Question 35

Solve the equation using the quadratic formula.

x2 + 14x + 85 = 0

{-1, -13}

{-7 + 6i}

{-7 + 6i, -7 – 6i}

{-7 – 36i, -7 + 36i}

Question 36

Add or subtract as indicated and write the result in standard form.

(6 – 2i) + (8 + 7i)

14 + 5i

-14 – 5i

-2 + 9i

14 – 5i

Question 37

Add or subtract as indicated and write the result in standard form.

(6 – 10i) + (7 + 7i) + (-4 – 5i)

13 – 3i

-5 – 22i

17 + 2i

9 – 8i

Question 38

Add or subtract as indicated and write the result in standard form.

(-5 + 3i) – 9

14 – 3i

4 – 3i

-14 + 3i

4 + 3i

Question 39

Add or subtract as indicated and write the result in standard form.

(3 – 4i) + (4 + 9i)

7 + 5i

7 – 5i

-7 – 5i

-1 + 13i

Question 40

Add or subtract as indicated and write the result in standard form.

4i – (-8 – i)

-8 + 3i

8 – 3i

8 + 5i

-8 – 5

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