Part 3
1. Be sure your work is shown and steps are in order.
2. List all the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor possible.
4. Identify complex roots if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations.
3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25
Answers
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
p(x) = (x +1)^2(2x -5)(x^2 -4x +5)
complex roots: 2±i
see the last attachment for a graph
Step-by-step explanation:
2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...
±(divisor of 25)/(divisor of 2)
That is, they are ...
±1/2, ±1, ±5/2, ±5, ±25/2, ±25
__
3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:
p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24
Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:
p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0
So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.
__
The reduced polynomial is ...
p1(x) = 2x^4 -11x^3 +17x^2 +5x -25
We already know that +1 is not a of it. Checking -1, we have ...
p1(-1) = 2 +11 +17 -5 -25 = 0
So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.
__
The reduced polynomial is ...
p2(x) = 2x^3 -13x^2 +30x -25
The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...
p2(1) = 2 -13 +30 -25 = 32 -38 = -6
The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.
The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).
__
The reduced polynomial is ...
p3(x) = x^2 -4x +5
This can be written in vertex form as ...
p3(x) = (x -2)^2 +1
The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.
The real solutions to p(x) are x = -1, -1, and 5/2.
__
4. The complex solutions will be the solutions to ...
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i . . . . complex roots of p(x)
__
5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.
The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.
The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
real solutions to p(x) are x = -1, -1, and 5/2.
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i complex roots
Related Questions
Associative
Property
Answers
Answer:
Below
Step-by-step explanation:
The associative property states that you can add or multiply numbers in any group.
Ex:
x + y + z = x + y + z
(x + y) + z = x + (y + z)
x * y * z = x * y * z
(x * z) * y = (x * y) * z
Addition: According to the associative property of addition, the sum of three or more numbers remains the same regardless of how the numbers are grouped or arranged. Here's an example of how the sum does NOT change irrespective of how the addends are grouped.
Multiplication: According to the associative property of multiplication, the product of three or more numbers remains the same regardless of how the numbers are grouped. Here's an example of how the product does not change irrespective of how the factors are grouped.
Division and Subtraction = NO ASSOCIATIVE PROPERTY
In Need OF HELP !!!!!!!!
Answers
What is the value of [2/3]-4
Answers
Answer:
option 4
Step-by-step explanation:
[tex]a^{-m}=(\frac{1}{a})^{m}\\\\\\(\frac{2}{3})^{-4}=(\frac{1}{\frac{2}{3}})^{4}\\\\=(\frac{3}{2})^{4}\\\\=\frac{3^{4}}{2^{4}}\\\\=\frac{81}{16}[/tex]
The number of calories in 5 cups of yogurt is 750. What proportion can you set up to determine the number of calories,c, in 9 cups of yogurt
Answers
Answer:
5 9
----- = ------
750 x
Step-by-step explanation:
Answer:
750 / 5 = c / 9
Step-by-step explanation:
How many real number solutions exist for 2x2 + 8x + 8 = 0?
A. 0
B. 1
C. 2
D. 3
Whats the answer i rlly need help
Answers
Answer:
B
Step-by-step explanation:
2x^2+8x+8=0
x^2+4x+4=0
(x+2)^2=0
so B, 1 solution
Pleaseee answer fast!!!! Solve the system of equation: y= 7/2x-3 and y= 7/2x +3
Answers
Answer:
The answer is no solution because these two lines have the same slope, meaning they are parallel. Parallel lines never intersect.
Answer:
No solution.
Step-by-step explanation:
Because y equals 7/2x-3, and 7/2x+3, we can say that both of these equations are equal to each other.
Thus, we have 7/2x-3=7/2x+3
(7/2)x-6=(7/2)x
x-6=x
-6=0
This is a false statement, so therefore this system of equations has no solution.
However, you can clearly see this as these lines are parallel lines as they have the same slope, 7/2. The solution to a system of equation is the intersecting point, but as we know about parallel lines they never intersect!
Hope this helps!
Given f(x) = -2x³ + x² - 2 find f(1)
Answers
Answer:
-3
Step-by-step explanation:
[tex]f(x)=-2x^3+x^2-2 \\\\f(1)=-2(1)^3+(1)^2-2= \\\\-2+1-2=\\\\-3[/tex]
Hope this helps!
The expression (x − 4)2 is equivalent to x2 − 16 x2 + 16 x2 − 8x + 16 x2 + 8x + 16
Answers
Answer:
Given below
Step-by-step explanation:
The algebraic identity is (a-b)^2
= a^2 + b^2 - 2ab
So it'll be,
(x-4)^2
= x^2 + (4)^2 - (2)(x)(4)
= x^2 -8x + 16
or x^2 +16 -8x
The expression x² + 16 -8x is equivalent to the given expression (x-4)². The correct answer would be an option (C).
What is algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
The expression is given in the question, as follows:
(x-4)²
As we know that the sum of square identity (a-b)² = a² + b² - 2ab
So x² + (4)² - (2)(x)(4)
x² -8x + 16 or
x² + 16 -8x
This expression is equivalent to the given expression.
Hence, the correct answer would be an option (C).
To learn more about the Algebra link is given below.
brainly.com/question/953809
#SPJ2
this camera stuff stinks but i need help on this
Answers
Answer: 4.2
Step-by-step explanation:
the coefficient is the number used to multiply a variable. here, the variable is x, and it is being multiplied by 4.2.
so the coefficient of the equation is 4.2
Solve for y: 5-3y - 8y = 121 *
Answers
Answer:
y= -116/11
Step-by-step explanation:
5-3y-8y=121
5-11y=121
5-5-11y=121-5
-11y=116
-11y/-11=116/-11
y= -116/11
City Middle School held its annual musical production last weekend. Of the 700 tickets sold, 55% were for the Saturday performance. How many tickets were sold for the Saturday show?City Middle School held its annual musical production last weekend. Of the 700 tickets sold, 55% were for the Saturday performance. How many tickets were sold for the Saturday show?
Answers
Answer: 385 tickets
Step-by-step explanation:
From the question, City Middle School held its annual musical production last weekend and of the 700 tickets that were sold, 55% were for the Saturday performance. The number of tickets that were sold for the Saturday show will be 55% of 700. This can be expressed mathematically as:
= 55% of 700
= 55/100 × 700
= 55 × 7
= 385 tickets
385 tickets were sold for the Saturday show.
Answer:
ITS IS A= 385
Step-by-step explanation:
What would be the answer and how would i get it?
Answers
Answer: c
Step-by-step explanation:
I very easy solve for x> then you take -3 -2 1,0 in order to get your answer
Answer:
x = {-3, -2, -1, 0, 1}
Step-by-step explanation:
We need to find the set that satisfies the inequality x > -4 ∩ x ≤ 1.
∩ means find the members that are common between two sets.
This means that we need to find the set of all integers that satisfy x > -4 and x ≤ 1
So, to find the low end, we find the lowest integer that satisfies x > -4, which is -3.
Now, to find the high end, we find highest integer that satisfies x ≤ 1, which is 1.
So x = {-3, -2, -1, 0, 1}
Can someone please help me with this?
Answers
Answer: x= -3 + 2[tex]\sqrt{2\\}[/tex] or -3 -2 [tex]\sqrt{2}[/tex]
Step-by-step explanation:
First you want to get the quadratic formula
in this case a=1 b=6 and c=1
plug it in and solve the equations
(sorry don't know how to put in equations here)
Answer:
Answer: x= -3 + 2\sqrt{2\\} or -3 -2 \sqrt{2}
Step-by-step explanation:
First you want to get the quadratic formula
in this case a=1 b=6 and c=1
plug it in and solve the equations
For which rational expressions is 5 an excluded value? Select two options.
X+5/X-5
x²-5/x² +5
X-3/x² - 25
2 x + 1/x2 + 25
X-5/
x² + 5x
Answers
Answer:
first one and the second one.
Step-by-step explanation:
nothing ：)
Answer:
this is right
Helen has only 10 questions left to do of her Math homework. She
has 120 minutes before it's her bedtime and it takes 5 minutes to do
each Math question. Describe the pattern and determine how much
time she will have available after her homework is complete.
A)Start at 120 and add 5 each time. She will have 70 minutes of free time after she finishes her math questions.
B) Start at 120 and subtract 5 each time. She will have 70 minutes of free time after she finishes her math questions.
C)Start at 120 and subtract 5 each time. She will have 75 minutes of free time after she finishes her Math questions.
D) Start at 120 and subtract 5 each time. She will not have enough time to complete all of her math questions.
Answers
B. Start at 120 and subtract 5 each time. She will have 70 minutes of free time after she finishes her math questions
. It takes Serina 15 seconds to drive to school. Her route is 16,000 meters long. What is Serina’s average speed on her route?
Answers
[tex]answer \\ = 1066.67m / s \\ solution \\ distance \: travelled = 16000 \: m \\ time \: taken = 15 \: seconds \\ speed = \frac{distance}{time} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{16000}{15} \\ \: \: \: \: \: \: \: \: \: \: \: = 1066.67 \: m/s \\ hope \: it \: helps[/tex]
Answer:
[tex] = 1,066.67m {s}^{ - 1} \\ [/tex]
Step-by-step explanation:
[tex]speed = \frac{distantce}{time} \\ = \frac{16000}{15} \\ = 1,066.67m {s}^{ - 1} [/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integ
Answers
What is the area of the rhombus shown below?
Answers
Answer:
A. 97.5 square units
Step-by-step explanation:
==>Given:
Rhombus ABCD with the following dimensions:
diagonal 1 (d1) = BD = 15
diagonal 2 (d2) = AC = 13
AB = 9.9
==>Required:
Area of the rhombus
==>Solution:
Since we know the length of the 2 diagonals, area of the rhombus can be calculated using A = ½ × d1 × d2
Area = ½ × 15 × 13
A = ½ × 195
A = 97.5 square units
Answer:
A
Step-by-step explanation:
pls help me 13 minute left 10 POINTS
Answers
Answer:
The answer is 6.28.
Step-by-step explanation:
The formula for finding the circumference is C=2 times 3.14 times the radius of the circle. 3.14 times 2 equals 6.28 times the radius which is 1 feet (because half of 2 feet equals 1 feet). 6.28 times 1 equals 6.28.
pls help me fast as u can
pls
Answers
Answer:
M5 W11 C1-CLASS ASSIGNMENT-LEVEL-1
I.Convert the following into minutes
a)2 hours 12 minutes 72
b)7 hours 45 minutes 465
II.Convert the following into seconds.
a)1 hour 4 minutes 26 seconds 3866
b)2 minutes 43 seconds 163
III.
a) 246 minutes= 4 hours 6 minutes
b) 117 seconds= 1 minutes 57 seconds
Step-by-step explanation:
if its wrong sorry i tried mmy best
The sum of the interior angles of a polygon is 8,100. How many sides does the polygon have?
Answers
Answer:
explanation below
Step-by-step explanation:
(n - 2) * 180 = 8100
n - 2 = 8100/180
n - 2 = 45
n = 45 + 2
n = 47 sides <---answer
happy to help ya :)
if james is 9years old and his sister rose is 15 years . what is the sum of their ages
Answers
Answer:
24 years
Step-by-step explanation:
James Age = 9 years
Rose's Age = 15 years
Sum of their Ages = 9+15
Sum of their Ages = 24 years
I will give you brainliest!!!! Which term best describes the slope of this line?
Answers
Answer:
zero
Step-by-step explanation:
The line is a horizontal line
Horizontal lines are of the form y= constant
This means they have zero slope
please help , factor 6x^2-33x+15 A. 3(2x-5)(x+1) B. 3(x+1)(2x+5) C. 3(2x-1)(x+5) D. 3(x-5)(2x-1)
Answers
Answer:
D
Step-by-step explanation:
Since the end term is positive, we know the 1 and 5 must both be positive or negative. However since -33x is negative, we know 1 and 5 are both negative too
Answer:
3(2x-1 )(x-5 )
Step-by-step explanation:
6x^2-33x+15
Factor out the greatest common factor
3(2x^2 -11x +5)
Factor inside the parentheses
3(2x )(x )
We need to get to -11 so the the only factors of 5 are 1 and 5 and they have to be negative
3(2x-1 )(x-5 )
2 * -5 + -1 = -10-1 = -11
Please explain and show work. In the function f(x)=cosx, f(x) is multiplied by a factor of 3, x is replaced with 4x and 5 is added to the function. Explain the effects this has on the graph of the function (i.e. horizontally, vertically, compressed, stretched, etc.).
Answers
Your graph will actually look like an oscillation (wave), it will be more compressed horizontally. As the value of x increases withe very whole number, your graph will compress horizontally. More like in the image below.
Can someone please explain what I did wrong here? Thank you!
Answers
Answer: The total number of ways is wrong. Since there is 12 members, each of them could be the president, vice president, etc.
Step-by-step explanation:
Can someone answer this question please please help me I really need it if it’s correct I will mark you brainliest .
Answers
Answer:
5 days
Step-by-step explanation:
Since the burrito stand uses 1/2 of a bag of tortillas, take 2 1/2 divided by 1/2 to find how many days the tortillas will last.
2.5/0.5 = 5 days
What are the answers? No hurry; I just have other things to do.
Answers
Answer:
what u need help with
Step-by-step explanation:
A cube has an edge length of 7 inches. What is its volume, in cubic inches?
Answers
Answer:
343 cubic inches
Step-by-step explanation:
7 times 7 times 7 is 343
Pls help with this (im not trying to be annoying)