Free Printable Chapter 4 Review

1.

Factor
m²+ 9m + 14

a)

(x + 7)(x + 2)

b)

(m + 14)(m + 1)

c)

m(m + 23)

d)

m(m + 9) + 14

2.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

3.

Solve by factoring: x² + 3x + 2 = 0

a)

x = 2 and x = -1

b)

x = -1 and x = -1

c)

x = -2 and x = -1

d)

x = 2 and x = 1

4.

Solve for n.

$5n^2+35=0$

a)

$\pm5i\ \sqrt[]{35}$

b)

$\pm\ \sqrt[]{-7}$

c)

$\pm i\ \sqrt[]{7}$

d)

$-i\ \sqrt[]{7}$

5.

Solve for x by factoring.
$x^2-4x=0$

a)

{2, 2}

b)

{0, 4}

c)

{-4}

d)

{4}

6.

Solve by factoring: x² - 4x - 12 = 0

a)

x = 1 and x = -12

b)

x = 6 and x = -2

c)

x = 4 and x = -3

d)

x = 6 and x = 2

7.

(x + 6)(x + 3)

a)

x²- 6x - 3

b)

x²+ 9x + 18

c)

x² + 9x - 18

d)

x² - 3x - 18

8.

(x + 5)(x - 8)

a)

x² - 3x + 40

b)

x²- 5x + 8

c)

x² - 3x - 40

d)

x² - 13x - 40

9.

(5 - 2i) + (-13 - 8i)

a)

-8 - 10i

b)

-18i

c)

8 - 10i

d)

-8 - 6i

10.

(5 + 2i)(1 + 3i)

a)

11 + 17i

b)

5 + 6i

c)

-1 + 17i

d)

-1

11.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

12.

(7 - 6i) + (9 + 11i)

a)

16 + 17i

b)

16 + 5i

c)

2 + 5i

d)

16 - 5i

13.

Multiply:
(6 – 4i)(6 + 4i)

a)

12 - 8i

b)

52i

c)

52

d)

$36-16i^2$

14.

Factor

$x^2-11x+18$

a)

(x + 9)(x - 2)

b)

(x - 9)(x - 2)

c)

(x - 6)(x - 3)

d)

(x - 9)(x - 9)

15.

$\sqrt[]{-16}$

a)

4i

b)

4

c)

$8i\ \sqrt[]{2}$

d)

$4i\ \sqrt[]{4}$

16.

Complete the square and rewrite.

$x^2+12x\ +\ c$

a)

$c=64;\ \left(x+8\right)^2$

b)

$c=36;\left(x-6\right)^2$

c)

$c=36;\left(x+6\right)^2$

d)

$c=16;\left(x+4\right)^2$

17.

SImplify:

(5 - 3i)²

a)

16 + 30i

b)

16 - 30i

c)

2 + 8i²

d)

2 + 8i

18.

Complete the square and rewrite.
x² - 20x + ____

a)

$c\ =\ 100;\ \left(x-10\right)^2$

b)

$c\ =\ 20;\ \left(x-10\right)^2$

c)

$c=100;\ \left(x+10\right)^2$

d)

$c=64;\left(x-8\right)^2$

19.

Complete the Square and rewrite.
x² + 11x + ____

a)

$c=\frac{121}{4};\left(x+\frac{11}{2}\right)^2$

b)

$c=\frac{121}{2};\left(x+\frac{11}{4}\right)^2$

c)

$c=\frac{121}{4};\left(x-\frac{11}{2}\right)^2$

d)

$c=121;\left(x+11\right)^2$

20.

What value of c would make this a perfect sqaure trinomial?
x² +8x + c

a)

4

b)

16

c)

64

d)

-16

21.

Use the quadratic formula to solve 2x² + 2x - 12?

a)

-2, 3

b)

2, 3

c)

2, -3

d)

-2, -3

22.

$x^2+2x-1=2$

a)

x = -1 and -3

b)

x = 1 and 3

c)

x = 1 and -3

d)

x = -1 and 3

23.

Solve Using the Quadratic Formula
x² + 4x - 40 = -8

a)

-10 & -4

b)

-4 & 10

c)

-8 & 4

d)

8 & -4

24.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

25.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

26.

What is the discriminant of -2x² − x − 1 = 0

a)

76

b)

-7

c)

9

d)

none of these

27.

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember: b² - 4ac

a)

400, 2 real root

b)

0, 1 real root with a multiplicity of 2

c)

-400, 2 imaginary roots

d)

-3, 2 imaginary roots

28.

$\sqrt{72}$

a)

$9\sqrt{8}$

b)

$6\sqrt{2}$

c)

$2\sqrt{6}$

d)

$\sqrt{72}$

29.

$\sqrt{-80}$

a)

$8i\sqrt{10}$

b)

$80i$

c)

$4i\sqrt{5}$

d)

$\sqrt{80}$

30.

Simplify

a)

± 4i √2

b)

± 4 √2

c)

± 2i √8

d)

± 2 √8

31.

Simplify

a)

± 2 √5

b)

± 4 √5

c)

± 5 √2

d)

± 5 √4

32.

$\sqrt[]{-56}$

a)

2i√14

b)

$8i\ \sqrt[]{7}$

c)

$7i\ \sqrt[]{8}$

d)

i√56

33.

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

34.

Find the vertex:

g\left(x\right)=2\left(x-4\right)^2+8

a)

( 4 , 8 )

b)

( -4 , -8 )

c)

( 4 , -8 )

d)

( -4 , 8 )

35.

Rewrite in vertex form
y=x²-10x-2

a)

y=(x+5)²+27

b)

y=(x-5)²+27

c)

y=(x-5)²-27

d)

y=(x+5)²-27

36.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

37.

Factor
4n²-17n-15

a)

(n-10)(6n+1)

b)

(4n-5)(n-3)

c)

(n-5)(4n-3)

d)

(n-5)(4n+3)

38.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

39.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

40.

6x²-x-2=0

a)

x= -2/3, 1/2

b)

x= 2/3, -1/2

c)

x= -2/3, -1/2

Chapter 4 Review

Total questions: 40

Worksheet time: 10hrs 0mins

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