Free Printable 2.5-2.6 Review

1.

The largest exponent determines the degree of the polynomial.

a)

True

b)

False

2.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

3.

What are the zeros of the polynomial and state their multiplicity at each.
y = (x - 5)(x + 2)²

a)

x = 5 multi 1, x = 2 multi 2

b)

x = -5 multi 2, x = -2 multi 1

c)

x = 5 multi 1, x = -2 multi 2

d)

x = 5 multi 2, x = -2 multi 1

4.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

5.

Identify the zeros:

a)

x=-2, x=-1, x=0

b)

x=-2, x=0

c)

x=-1, x=0, x=2

d)

x=-2, x=0, x=1

6.

a)

a

b)

b

c)

c

d)

d

7.

Which equation could represent the graph?

a)

y=-(x+1)(x-2)(x-4)

b)

y=(x+1)²(x-3)(x-1)³

c)

y = 3x³ – 2x + 1

d)

y=(x+1)³(x-3)(x-1)²

8.

Which equation could represent the graph?

a)

y=-(x+1)(x-2)(x-4)

b)

y=(x+1)²(x-3)(x-1)³

c)

y = 3x³ – 2x + 1

d)

y=(x+1)³(x-3)(x-1)²

9.

Which solution has a multiplicity of 2?

a)

-1

b)

1

c)

3

d)

none of them do

10.

What is the correct graph of the function?

a)

b)

c)

d)

11.

Solve the following polynomial.

Resuelve el siguiente polinomio

$0=x^3-3x^2-4x+12$ (select all that apply)

a)

$x=\pm2$

b)

$x=3$

c)

$x=1$

d)

$x=0$

12.

Find the zeros

Encuentra los ceros.

. $g\left(x\right)=3x^3-15x^2-72x$ (select all that apply)

a)

$x=-3$

b)

$x=8$

c)

$x=-7$

d)

$x=0$

e)

$x=3$

13.

Find all zeros for the polynomial

Encuentra todos los ceros para el polinomio

P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

14.

Find all zeros for the polynomial

Encuentra todos los ceros para el polinomio

f(x) = x⁴+8x²-9

a)

-1, ⅓, ±3i

b)

½, -1, ±3i

c)

1, -1, ±i√11

d)

1, -1, ±3i

15.

Find the values of the zeros of the function

Encuentra los valores de los ceros de la función.

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

a)

x=-2, x=3, x=5/3

b)

x=2, x=-3, x= -5/3

c)

x=-2, x=3, x=3/5

d)

x=2, x=-3, x=-3/5

16.

Solve: choose all that apply.

Resuelva: elija todas las que correspondan.

x³ + 2x² + 5x + 10 = 0

a)

-2

b)

2

c)

-i√5

d)

i√5

e)

0

17.

Solve for x:

Solución para x:

$\left(x^2+1\right)\left(x^2-5\right)=0$

a)

$x\ =\left\{\ \sqrt[]{5},\ \ \pm\ 1\right\}$

b)

$x=\ \left\{\ \pm\ 1,\ \pm\ 5\right\}$

c)

$x\ =\left(\ \pm\ 1i\ \ ,\ \ \pm\ \sqrt[]{5}\right)$

d)

$x=\ \left\{\pm\ 1\ i\ ,\ \ \sqrt[]{5}\right\}$

18.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

19.

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial.

a)

A

b)

B

c)

C

d)

D

20.

What is the degree of a polynomial that has roots of -2, 4i and -4i ?

a)

3

b)

4

c)

1

d)

2

21.

If 2i is a zero, then

a)

2i repeats twice

b)

-2i is a zero too

c)

1-2i is a zero too

d)

0+2i is a zero too

22.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

23.

Using the following roots, write in factored form.

-6, √6, 3

a)

(x+6)(x+√6)(x-3)

b)

(x-6)(x-√6)(x+3)

c)

(x+6)(x-√6)(x+3)

d)

(x+6)(x-√6)(x-3)

24.

Write in factored form using the following roots.

7, -2i

a)

(x-7)(x-2i)

b)

(x-7)(x+2i)(x-2i)

c)

(x-7)(x+2i)

d)

(x-7)(x+7)(x-2i)

25.

All zeros containing a square root sign comes in pairs.

a)

True

b)

False

26.

Write the equation of the quadratic

whose roots are -4, -2.

a)

x²-6x+8

b)

x²+6x+8

c)

x²-4x-2

d)

x²-2x-4

27.

Which of the following would be the correct factored form with roots 2, 5i, and 6?

a)

(x-6)(x-2)(x+5i)(x-5i)

b)

(x+6)(x+2)(x+5i)

c)

(x-6)(x-2)(x-5i)

d)

(x+6)(x+2)(x-5i)

28.

If a+bi is a root of a polynomial, then _______ is also a root.

a)

i²

b)

a-bi

c)

a+bi

d)

-i²

2.5-2.6 Review

Total questions: 28

Worksheet time: 1hrs 29mins

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