2.2-2.4 Test

Question 0

Leading Coefficient Test

f(x)=3/4(x⁴+3x²+2)

Answer 0

Left side up

Right side up

Question 1

Leading Coefficient Test

f(x)=-x²+6x+9

Answer 1

Left side down

Right side down

Question 2

Finding Zeros

f(x)=2x²+11x-21

Answer 2

0=(2x-3)(x+7)

Zeros; 3/2, -7

Question 3

Finding Zeros

f(x)=-12x³+20x²

Answer 3

0=-x²(12x-20)

Zeros; 0, 5/3

Question 4

Finding Zeros

f(t)=t³-3t

Answer 4

0=t(t+√(3))(t-√(3))

Zeros; 0, ±√(3)

Question 5

Intermediate Value Theorem

f(x)=3x³-x²+3

Answer 5

(-1,0)

Question 6

Intermediate Value Theorem

f(x)=x⁴-5x-1

Answer 6

(-1,0) (1,2)

Question 7

Long Division to Divide Polynomials

24x²-x-8)/(3x-2

Answer 7

8x+5+(2/(3x-2))

Question 8

Long Division to Divide Polynomials

5x³-13x²-x+2)/(x²-3x+1

Answer 8

5x+2

Question 9

Long Division to Divide Polynomials

X⁴-3x³+4x²-6x+3)/(x²+2

Answer 9

X²-3x+2-(1)/(x²+2)

Question 10

Using Synthetic Division to Divide Polynomials

6x⁴-4x³-27x²+18x)/(x-(2/3)

Answer 10

6x³-27x

Question 11

Using Synthetic Division to Divide Polynomials

2x³-19x²+38x+24)/(x-4

Answer 11

2x²-11x-6

Question 12

Using Synthetic Division to Prove Factors
f(x)=20x⁴+9x³-14x²-3x
A) x=-1
B) x=3/4
C) x=0
D) x=1

Answer 12

A)yes
B)yes
C)yes
D)no

Question 13

Using Synthetic Division to Find the Value of the Function
f(x)=x⁴+10x³-24x²+20x+44
A) f(-3)
B) f(-1)

Answer 13

A)-421

B)-9

Question 14

A) verify given factors
B) find remaining factors
C) use your results to write the complete factorization
D) list all zeros
E) check it by putting the original function and your answer to part c into a graphing utility, and graphing them on the same plane
f(x)=x⁴-4x³-7x²+22x+24
(x+2)(x-3)

Answer 14

A) if you got this far, good job 
B) (x+1),(x-4)
C) f(x)=(x+2)(x+1)(x-4)(x-3)
D) -2,-1,4,3
E) I could really care less

Question 15

A) verify given factors
B) find remaining factors
C) use your results to write the complete factorization
D) list all zeros
E) check it by putting the original function and your answer to part c into a graphing utility, and graphing them on the same plane
f(x)=x³+4x²-25x-28
(X-4)

Answer 15

A) good job for getting this far!
B) (x+7),(x+1)
C) f(x)=(x+7)(x+1)(x-4)
D) -7, -1, 4
E) do it if you care to

Question 16

Write the complex number in standard form

3-√(-25)

Answer 16

3-5i

Question 17

Write the complex number in standard form

-5i+i²

Answer 17

-1-5i

Question 18

Perform the operation. Result in standard form.

(√(2)/2)-(√(2)/2)i)-((√(2)/2)+(√(2)/2)i

Answer 18

-i√(2)

Question 19

Perform the operation. Result in standard form.

1+6i)(5-2i

Answer 19

17+28i

Question 20

Perform the operation. Result in standard form.

i(6+i)(3-2i)

Answer 20

9+20i

Question 21

Perform the operation. Result in standard form.

3+2i)/(5+i

Answer 21

(17/26)+(7/26)i

Question 22

Perform the operation. Result in standard form.

1/(2+i))-(5/(1+4i

Answer 22

(9/85)+(83/85)i

Question 23

Write a polynomial given the zeros

0,10

Answer 23

x(x-10)
Or
x²-10x

Question 24

Write a polynomial given the zeros

2,-6

Answer 24

(x-2)(x+6)
Or
x²+4x-12

Question 25

Write a polynomial given the zeros

0,-2,-3

Answer 25

x(x+2)(x+3)
Or
x³+5x²+6x

Question 26

Write a polynomial given the zeros

4,-3,3,0

Answer 26

x(x-4)(x+3)(x-3)
Or
x⁴-4x³-9x²+36x

Question 27

Write a polynomial given the zeros

1+√(3),1-√(3)

Answer 27

x²-2x-2

Question 28

Find a polynomial of degree n with given zeros
Zeros=-2
N=2

Answer 28

x²+4x+4

Question 29

Find a polynomial of degree n with given zeros
Zeros=-3,0,1
N=3

Answer 29

x³+2x²-3x

Question 30

Find a polynomial of degree n with given zeros
Zeros=0,√(3),-√(3)
N=3

Answer 30

x³-3x

Question 31

Find a polynomial of degree n with given zeros
Zeros=-5,1,2
N=4

Answer 31

x⁴+x³-15x²+23x-10

Question 32

Find a polynomial of degree n with given zeros
Zeros=0,-4
N=5

Answer 32

x⁵+16x⁴+96x³+256x²+256x

Question 33

what are the equations for finding the square roots of complex numbers?

Answer 33

(a+bi)²=x+yi
a²-b²=x
a²+b²=√(x²+y²)