Free Printable A2 OPTIONAL Test 5 Review: Polynomial Equations

1.

45=10p+5

a)

$p=4$

b)

$p=5$

c)

$p=-5$

d)

$p=-4$

2.

7w-2=26

a)

$w=4$

b)

$w=3$

c)

$w=-3$

d)

$w=-4$

3.

In order to solve an equation, we must get variables on side of an equation, and constants on the opposite side.

a)

True

b)

False

4.

12v-2+2v+7=33

a)

$v=2$

b)

$v=4$

c)

$v=1$

d)

$v=3$

5.

Choose the best method to solve this quadratic:

(a)

3x²- 21 = 3

a)

Square Roots

b)

ZPP

c)

Quadratic Formula

6.

Choose the best method to solve this quadratic:

(a)

-3 = 4x²+ 9x

a)

Quadratic Formula

b)

Square Roots

c)

ZPP

7.

Choose the best method to solve this quadratic:

(a)

x²+ 8x - 13 = 0

a)

Square Roots

b)

ZPP

c)

Quadratic Formula

8.

Choose the best method to solve this quadratic:

(a)

x²- 7x + 12 = 0

a)

ZPP

b)

Square Roots

c)

Quadratic Formula

9.

Choose the best method to solve this quadratic:

(a)

2(x + 2)² - 5 = 8

a)

Square Roots

b)

Quadratic Formula

c)

ZPP

10.

Choose the best method to solve this quadratic:

(a)

x² - 8x - 5 = 0

a)

ZPP

b)

Square Roots

c)

Quadratic Formula

11.

Charlie is solving $3x^2+5x=12$ by factoring. Which of the following describes what his first step should be?

a)

A.

Divide both sides f the equation by 3.

b)

B.

Take the square root of both sides of the equation.

c)

C.

Subtract 12 from both sides of the equation.

d)

D.

Find two values with a sum of 5 and a product of 12.

12.

Which method of solving quadratics would you use to solve the following:

$12x^2-7\ =41$

a)

Completing the Square

b)

ZPP

c)

Square Roots

13.

Which method of solving quadratics would you use to solve the following:

$12\left(x+5\right)^2-7\ =41$

a)

Completing the Square

b)

ZPP

c)

Square Roots

14.

What mathematical process did they use?

a)

Square Roots

b)

Quadratic Formula

c)

ZPP

15.

In the quadratic formula, the expression
b²-4ac is called

a)

discrim

b)

determinant

c)

discriminant

d)

none of these

16.

If 3+2i is a solution of a quadratic equation, then other solution of this quadratic equation is

a)

2-3i

b)

3+2i

c)

1/3 -1/2i

d)

3-2i

17.

Solve for the values of x:

(2x + 5)(5x - 2) = 0

a)

x= -5/2, x= -2/5

b)

x= -5/2, x= 2/5

c)

x= 5/2, x= 2/5

d)

x= 5/2, x= -2/5

18.

Find all the solutions for x when

x²+ 9x - 36 = 0

a)

(x + 12)(x - 3)

b)

x = 12 and x = -3

c)

x = -12 and x = 3

d)

(x - 9)(x - 4)

19.

Solve and find your x-intercepts:
0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

20.

The solutions of the quadratic equation
x²+2x-15=0 are

a)

x = 3 or x = 5

b)

x = 5 or x = -3

c)

x = -5 or x = 3

d)

x = -3 or x = -5

21.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

22.

Solve by taking square roots:

5m² + 1 = 6

a)

m = 1

b)

m = 1 or -1

c)

m = √7

d)

m = 7/5 m = -7/5

23.

Solve:
x² - 49 = 0

a)

x = -7, x = 7

b)

x = -7

c)

x = 7

d)

x = -7, x = 1

24.

Solve by taking square roots.
$x^2-225=0$

Hint: Isolate $x^2.$

a)

$\left\{\pm\ 14\right\}$

b)

$\left\{15\right\}$

c)

$\left\{\pm\ 15\right\}$

d)

$\left\{112.5\right\}$

25.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

26.

Solutions of a quadratic equation are also called

a)

roots

b)

x-intercepts

c)

zeros

d)

All of the above

27.

The first step in solving quadratic equations is to . . .

a)

factor

b)

write the equation in standard form

c)

use quadratic formula

d)

complete the square

28.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

29.

What is this formula?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

30.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

31.

Solve the following for x by using the Quadratic Formula

2x²+6x=7

a)

b)

c)

32.

Your Turn!

\sqrt{-9}

a)

$\pm3$

b)

$\pm3i$

c)

$\pm9i$

d)

$\pm9$

33.

Solve the following equation using the quadratic formula: $5x^2-6=13x$

a)

$x=-2,\ x=-\frac{3}{5}$

b)

$x=2,\ x=\frac{3}{5}$

c)

$x=3,\ x=-\frac{2}{5}$

d)

undefined

34.

Solve the following equation using the quadratic formula:

$3x^2+16x+5=0$

a)

$x=\frac{1}{3},\ x=5$

b)

$x=-\frac{1}{3},\ x=-5$

c)

$x=-1,\ x=-15$

d)

$x=1,\ x=15$

35.

$x^2+81=0$

a)

$\pm\sqrt{9i}$

b)

$\pm9$

c)

$\pm9i$

d)

$\pm3i$

36.

$\sqrt{-1}=$

a)

$i$

b)

$-1$

c)

$-i$

d)

$1$

37.

$\sqrt{-64}$

a)

$8i$

b)

$-8$

c)

$8$

d)

$\pm8i$

38.

$\left(3-i\right)-\left(2+4i\right)=$

a)

$10+10i$

b)

$1-5i$

c)

$6-4i^2$

d)

$10$

39.

$\sqrt{-12}$

a)

$2i\sqrt{3}$

b)

$4i\sqrt{3}$

c)

$-2\sqrt{3}$

d)

$-4i\sqrt{3}$

40.

What is the imaginary number in this number:

6+3i

a)

6

b)

3

c)

3i

d)

6+3i

41.

(4+i)+(7-5i)

a)

5i+2i

b)

11+6i

c)

11-4i

d)

7i

42.

(7+i)(4-i)

a)

29-3i

b)

11-i^2

c)

$28-i^2$

d)

27- 3i

43.

x²+4x-32=0

a)

x= -8, 4

b)

x= 8, -4

c)

x= -8, -4

44.

x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

45.

What are terms separated by?

a)

multiplication

b)

addition or subtraction

c)

division

d)

a number

46.

How do you determine the degree of a trinomial

a)

coefficient

b)

smallest exponent

c)

variable

d)

largest exponent

47.

What is another name for solutions of a polynomial?

a)

coefficient

b)

factors

c)

zeros

d)

equations

48.

f(x)=(x+4)(x-3)(x-2)
List the zeros for this function.

a)

x=-4, x=3, x=-2

b)

x= 4, x=3, x=2

c)

x=-4, x=3, x=2

d)

x=4, x=3, x=2

49.

5w²-5w=0

a)

w=0 and w=-1

b)

w=0 and w=1

c)

w=1 and w=-1

d)

w=1 and w=5

50.

Solve the polynomial equation:

x² + 15x + 64 = 20

a)

x = -8, 2

b)

x = -7, 5

c)

x = -11, -4

d)

x = -11

51.

Which one of these is in standard form?

a)

x⁴ + 25x²- 10x³

b)

x⁴ - 10x³ + 25x²

c)

- 10x³ + 25x²+ x⁴

d)

25x²+ x⁴ - 10x³

52.

State the degree of the polynomial:
f(x) = 2x⁴ + 19x² + 24

a)

1

b)

2

c)

3

d)

4

53.

What are two solutions to the polynomial:
x²+14x=0

a)

x=0, x= 14

b)

x=-14

c)

x= 1, x =10

d)

x= -14, x = 0

54.

Solve (x²-9) = 0

a)

x = 9

b)

x = 9, -9

c)

x = 3, -3

d)

x = 3

55.

Solve.
$n^3-2n=0$

a)

$0,\ \pm\sqrt{2}$

b)

$\pm\sqrt{2}$

c)

$0,\ 2,\ 2$

d)

$\sqrt{2},\ 0$

56.

Solve: $x^4-100x^2=0$

a)

$\pm50,\ 0$

b)

$0,\ 10$

c)

$0,\ 0,\ -10,\ 10$

d)

$0,\ 100$

57.

Solve the equation in the real number system.

$2x^3-x^2-12x+6=0$

a)

$\left\{\frac{1}{2},\sqrt[]{6},-\sqrt[]{6}\right\}$

b)

$\left\{-\frac{1}{2},\sqrt[]{6},-\sqrt[]{6}\right\}$

c)

$\left\{2,\sqrt[]{6},-\sqrt[]{6}\right\}$

d)

$\left\{-2,\sqrt[]{6},-\sqrt[]{6}\right\}$

58.

Solve $2x\left(x-1\right)=7x^2-3x$

a)

$\left\{-\frac{1}{5},\ 0\right\}$

b)

$\left\{0,\ \frac{1}{5}\right\}$

c)

$\left\{0,\ 5\right\}$

d)

$\left\{-5,\ 0\right\}$

59.

Solve the following polynomial. $0=x^3-3x^2-4x+12$

(select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

60.

Solve the polynomial equation by factoring: $x^4+x=0$

a)

$x=\pm1,\pm i$

b)

$x=0,-1,\frac{1\pm i\sqrt{3}}{2}$

c)

$x=0,-1,\frac{-1\pm i\sqrt{3}}{2}$

d)

$x=1,1\pm2i\sqrt{3}$

A2 OPTIONAL Test 5 Review: Polynomial Equations

Total questions: 60

Worksheet time: 4hrs 40mins

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