Which of the following is NOT a linear factor of the polynomial function?
f (x) = x^3 – 5x^2 - 4x + 20
F. (x + 5)
G. (x - 2)
H. (x - 5)
J. (x + 2)

Answers

Answer 1

Answer:

Among the four choices, [tex](x + 5)[/tex] is the only one that is not a linear factor of this polynomial function.

Step-by-step explanation:

Let [tex]a[/tex] denote some constant. A linear factor of the form [tex](x - a)[/tex] is a factor of a polynomial [tex]f(x)[/tex] if and only if [tex]f(a) = 0[/tex] (that is: replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]a\![/tex] would give this polynomial a value of [tex]0[/tex].)

For example, in the second linear factor [tex](x - 2)[/tex], the value of the constant is [tex]a = 2[/tex]. Verify that the value of [tex]f(2)[/tex] is indeed [tex]0[/tex]. (In other words, replacing all [tex]x[/tex] in the polynomial [tex]f(x) \![/tex] with the constant [tex]2[/tex] should give this polynomial a value of [tex]0\![/tex].)

[tex]\begin{aligned}f(2) &= 2^3 - 5\times 2^2 - 4 \times 2 + 20 \\ &= 8 - 20 - 8 + 20 \\ &= 0 \end{aligned}[/tex].

Hence, [tex](x - 2)[/tex] is indeed a linear factor of polynomial [tex]f(x)[/tex].

Similarly, it could be verified that [tex](x - 5)[/tex] and [tex](x + 2)[/tex] are also linear factors of this polynomial function.

Rewrite the first linear factor [tex](x + 5)[/tex] in the form [tex](x - a)[/tex] for some constant [tex]a[/tex]: [tex](x + 5) = (x - (-5))[/tex], where [tex]a = -5[/tex].

Calculate the value of [tex]f(5)[/tex].

[tex]\begin{aligned}f(5) &= (-5)^3 - 5\times (-5)^2 - 4 \times (-5) + 20 \\ &= (-125) - 125 + 20 + 20 \\ &= -210\end{aligned}[/tex].

[tex]f(5) \ne 0[/tex] implies that [tex](x - (-5))[/tex] (which is equivalent to [tex](x + 5)[/tex]) isn't a linear factor of this polynomial function.


Related Questions

Please help me to find out this question .This question is from chapter simple Interest
PRINCIPLE=₹2630
RATE=8%
TIME=2 1/Fund the S.I and amount ​

Answers

Answer:

The simple interest is of 526.

The total amount is 3156.

Step-by-step explanation:

Simple Interest

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

[tex]T = E + P[/tex]

In this question, we have that:

[tex]P = 2630, I = 0.08, t = 2.5[/tex]

The simple interest is:

[tex]E = P*I*t = 2630*0.08*2.5 = 526[/tex]

The simple interest is of 526.

The total amount is:

[tex]T = E + P = 2630 + 526 = 3156[/tex]

The total amount is 3156.

Someone help me
Right now.

Answers

28 is the answer haha


Form a paragraph proof for the following. Make sure you include all the
explanations.
HELP ASAP PLS

Answers

Answer:

Line BD is Congruent to Line BD due to the Reflexive property. Angle Bad is congruent to angle BCD because of the third angle theorem therefore triangle ABD is congruent to triangle CBD because all angles and sides are congruent

I don't know if that will satisfy your teacher because some prefer different things but that leaves no ground to be inferred and explains everything word for word.

Daniels mom gave him $8 for his allowance He wants to buy new shoelaces for his vans that cost $5. What percentage of his money will Daniel spend on the new shoelaces?

Answers

75% cus u divide the denominator by the numerator is 5 and 8

Convert the angle −4.5 radians to degrees, rounding to the nearest 10th

Answers

-4.5 rad = -4.5 x 180 / pi = -257.83°

Answer:-257.8

Step-by-step explanation:

If i put a 100$ into the stock market and the stock market increase by 2% per year. how much money would i have after a year

Answers

Answer:

$102

Step-by-step explanation:

2% of $100 = 0.02 * $100 = $2

The increase is $2.

$100 + $2 = $102

Answer: $102

Answer:

100 x 0,2 x 1 year(12/12 months)

=$102 after a year

Can you help me here is the inage

Answers

Answer:

150x=y

Step-by-step explanation:

2x150=300

4x150=600

6x150=900

8x150=1200

The diagram below shows some measurements taken from a new bridge. How long is the bridge?

 feet   


Answers

Answer:

1,737.3 feet

Step-by-step explanation:

Let's assume the length of the bridge consists of 2 right triangles as shown in the diagram. Use pythagorean theorem to find the other missing leg of each right triangle.

Let the missing leg for each triangle be x and y respectively.

Length of bridge = x + y

✔️x = √(1115² - 860²) = √503,625

x ≈ 709.7 (nearest tenth)

✔️y = √(1340² - 860²)

y ≈ 1,027.6 (nearest tenth)

✔️ Length of bridge = 709.7 + 1,027.6 = 1,737.3 ft

Marking brainliest!!

What should I put for the second question? I am confused. HELPP

Answers

if other experts state the same thing in their own paper or document.

One could analyze the ideas expressed in papers and lectures of experts. Since these people are well educated and creditable, their ideas should be taken seriously. In this case, the author argues that people should pay for the things that they own. By finding a credible expert that shares the same opinion, the idea can be verified.

I need help please ASAP ?!!!!!!!

Answers

Answer:

B

Step-by-step explanation:

B because the number line goes from negative 6, -2, and x must be greater than negative 6 but less than or equal to 2

Nicki needs to purchase AT LEAST 65 party decorations. The Party Palace charges
$0.50 per decorative streamer and $0.25 per balloon, including tax. Which
combination of streamers and balloons can Nicki purchase with $20.00 at the Party
Palace?

Answers

Answer:

B

Step-by-step explanation:

B is the most likely answer due to

13x.5=6.5

and

53x.25=13.25

13.25+6.5=19.75$

Now stop making a high schooler do your work xD

Jill wants to solve the following system using the elimination method:
Y = X + 8
y = 3x - 11
What number should the equation = x + 8 be multiplied by to eliminate x?
3

Answers

Answer:

3

Step-by-step explanation:

y= x + 8..... (1)

y= 3x - 11..... (2)

y - x = 8..... (3)

y - 3x = -11..... (4)

eliminating x:

(3) × 3: 3y - 3x = 24 ........ (5)

(4) × 1: y - 3x = -11 ......... (6)

(5) - (6): 2y = 35

Divide both sides by 2, therefore, y = 17.5

substitute the value of y into (3)

y - x = 8

17.5 - x = 8

17.5 - 8 = x

9.5 = x

I hope it'll help

2) Apply the distributive property to solve the following.
(15 + 12) - 5
Answer:

Answers

Answer:

22

Step-by-step explanation:

15+12=27

27-5=22

4(A) The table given shows the change in price in a sale.
TV
Laptop
Normal
Dhs 2000
Dhs 1800
price
Sale price
Dhs 1750
Dhs 1440
(a) Calculate the percentage increase or decrease for
(0) TV and
) Laptop
(b) Which item has the best reduced price?
Cho can anyone help me ​

Answers

Answer:

(a)

[tex]\%Decrease= 12.5\%[/tex] --- TV

[tex]\%Decrease= 20\%[/tex] --- Laptop

(b) Laptop

Step-by-step explanation:

Given

Normal                       Sales

[tex]TV = 2000[/tex]                  [tex]TV = 1750[/tex]

[tex]Laptop = 1800[/tex]             [tex]Laptop = 1440[/tex]

Solving (a): Percentage increase of decrease for both

Percentage change is calculated as:

[tex]\%Change = \frac{New - Old}{Old} * 100\%[/tex]

For TV

[tex]\%Change = \frac{1750 - 2000}{2000} * 100\%[/tex]

[tex]\%Change = \frac{-250}{2000} * 100\%[/tex]

[tex]\%Change = -0.125* 100\%[/tex]

[tex]\%Change = -12.5\%[/tex]

It is a decrease because it is negative

[tex]\%Decrease= 12.5\%[/tex]

For Laptop

[tex]\%Change = \frac{1440 - 1800}{1800} * 100\%[/tex]

[tex]\%Change = \frac{-360}{1800} * 100\%[/tex]

[tex]\%Change = -0.2* 100\%[/tex]

[tex]\%Change = -20\%[/tex]

It is a decrease because it is negative

[tex]\%Decrease= 20\%[/tex]

Solving (b):

Laptop has the best reduced price  because it has a larger percentage decrease

By what percent will a fraction increase is decreased by 10% and its denominator is decreased by 50%

Answers

Answer:

Let's assume the fraction is 1/1

decreasing 1 by 10% = .9

decreasing 1 by 50% = .5

So the fraction becomes .9/.5 = 1.8

So its value increases by 180%

Step-by-step explanation:

If 6 times a certain number is added to 8, the result is 32. Which of the following equations could be used to solve the problem? 6 x = 8 + 32 6 x+8 = 32 6 x= 32 61 X + 8) = 32​

Answers

Answer:

6x + 8 = 32

6(x + 8) = 32

Step-by-step explanation:

Hope this helps

Line k is the perpendicular bisector of pq and point r which of the following statements must be true?

Answers

Answer:

question incomplete.

Step-by-step explanation:

assume that the weight of ripe watermelons grown at a particular farm are normally distributed witha mean of 20 pounds and a standard deviation of 1.4 pounds. determine the percent of watermelons that weigh between 18.48 pounds and 22.68 pounds

Answers

Answer:

The answer is "78.25%"

Step-by-step explanation:

Given:

[tex]\mu =20\\\\\sigma=1.4[/tex]

[tex]p(18.48<x<22.63)=p(\frac{18.48-20}{1.7}<\frac{\bar{x}-\mu}{\sigma}<\frac{22.63-20}{1.4})\\\\[/tex]

                                 [tex]=p(\frac{-1.52}{1.7}<Z<\frac{2.63}{1.4})\\\\=p(-0.89<Z<1.87)\\\\[/tex]

                                 [tex]=p(Z<1.87)-p(Z<-0.89)\\\\[/tex]

                                 [tex]=0.969258-0.1867329\\\\=0.7825251\\\\=78.25 \%[/tex]

Which function is shown in the graph below?

On a coordinate plane, an exponential function shows decay. It rapidly decreases into quadrant 1 and approaches y = 1 in quadrant 1.
y = (one-half) Superscript x + 3 Baseline minus 1
y = (one-half) Superscript x minus 3 Baseline + 1
y = (one-half) Superscript x minus 1 Baseline + 3
y = (one-half) Superscript x + 1 Baseline minus 3

Answers

Answer:

Option B, y = 2 Superscript x + 2 Baseline + 3

Step-by-step explanation:

I could be wrong tbh. I graphed it on a graphing website and the graph from B matched up with the graph shown in the question.

Hope this helps Bye =)

The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]

Exponential function

An exponential function is in the form:

y = abˣ

Where y,x are variables, a is the initial value of y and b is the multiplication factor.

The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]

From the point (0, 9):

[tex]y=(\frac{1}{2})^{0-3} +1=9[/tex]

Also at point (3, 2):

[tex]y=(\frac{1}{2})^{3-3} +1=2[/tex]

Find out more on Exponential function at: https://brainly.com/question/12940982

help 20 points on the line real answer plz!!

Answers

Step-by-step explanation:

D makes the most sense to me hopefully this helps

Answer:

24 cubic in

Step-by-step explanation:

Hope this helps UwU

Homework
Answers are given at the end of
the chapter
Q1 Change 0.035 g to milligrams.​

Answers

Answer:

the answer 0.035 g = 35 milligrams

Answer:

Step-by-step explanation:

35miligram in 0.035g

The phenomenon of bottle flipping has hit the nation. You design a machine that can randomly flip a bottle. You observe 2180 random, independent flips, and 325 land the correct way. Estimate the overall proportion of bottles that land correctly when flipped randomly. Use a 98% confidence level. Round everything to 3 decimal places. a) State the parameter of interest. Verify that the necessary conditions are present in order to carry out the procedure.

Answers

Answer:

The variable of interest is the proportion of flips that land the correct way when flipped randomly.

The necessary conditions [tex]n\pi \geq 10[/tex] and [tex]n(1-\pi) \geq 10[/tex] are present.

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

Step-by-step explanation:

Variable of Interest:

Proportion of flips that land the correct way when flipped randomly.

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Necessary conditions:

The necessary conditions are:

[tex]n\pi \geq 10[/tex]

[tex]n(1-\pi) \geq 10[/tex]

You observe 2180 random, independent flips, and 325 land the correct way.

This means that [tex]n = 2180, \pi = \frac{325}{2180} = 0.149[/tex]

Necessary conditions

[tex]n\pi = 2180*0.149 = 325 \geq 10[/tex]

[tex]n(1-\pi) = 2180*0.851 = 1855 \geq 10[/tex]

The necessary conditions [tex]n\pi \geq 10[/tex] and [tex]n(1-\pi) \geq 10[/tex] are present.

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.33[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 - 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.131[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.149 + 2.33\sqrt{\frac{0.149*0.851}{2180}} = 0.167[/tex]

The 98% confidence interval for the overall proportion of bottles that land correctly when flipped randomly is (0.131, 0.167).

Write an equation for this tape diagram 6th grade math help pls thanks if you do

Answers

Answer: x(15x)

Step-by-step explanation:

What is the ratio of 18 inches to 1 yard? (Change 1 yard to 36 inches before writing the ratio)

Answers

Answer:

1:2

Step-by-step explanation:

18 inches to 1 yard

We need to convert 1 yard to 36 inches

18 inches : 36 inches

Divide each side by 18

18/18 : 36/18

1:2

Question 27
27. If an increase in one quantity brings about a corresponding decrease in the
other and vice versa, then the two quantities vary
a) sometimes directly and sometimes inversely b) directly
c) inversely d) none of these
ОА
Ов
Ос
OD​

Answers

Answer:

c) inversely

Step-by-step explanation:

In Mathematics an inverse relationship can be defined as a relationship between two variables, in which an increase in the value of one variable leads to a decrease in the value of the other variable i.e as the value of one variable becomes large, the value of the other variable becomes small.

Mathematically, an inverse relationship is given by the formula;

A = K/B

Where;

A and B are the variables.

K is the constant of proportionality.

Hence, if an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.

In the Special Right Triangle below, solve for the value of x. X = _____ (keep your answer in simplest radical form)

Options
6
6√3
6√6
12
12√2
18
12√3

Answers

Answer:

Step-by-step explanation:

It's a 30-60-90 triangle. The sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 90° angle is 12√3, so the side opposite the 30° is (12√3)/2 = 6√3.

The side opposite the 60° angle is (6√3)√3 = 18

x = 18

y = 6√3

Answer:

x = 18

y = 6√3

Step-by-step explanation:

<3

Help Please!!!
Thanks

Answers

it’s a!! you can check by replacing x with the numbers inside the brackets until the equality is true!

Answer:

d i hope please be d please please

A salt shaker company produces salt shakers of various heights they create a table showing how many salt Greynolds each size salt shaker holt does the star represent a proportional relationship click on the correct response then answer the question below

Answers

You can ask for a tutor here on the Brainly app don’t forget!!!! :)

Suppose that P(n) is a propositional function. Determine for which improper subset of the domain of n the statement P(n) must be true if a) P(0) is true; for all nonnegative integers n, if P(n) is true, then P(n 2) is true. b) P(0) and P(1) are true; for all nonnegative integers n, if P(n) and P(n 1) are true, then P(n 2) is true

Answers

Answer:

a) P(n) is true for all 'n' in the set ; { 0,2,4,6,8 ….. }

b) P(n) is true for all 'n' in the set ; { 0,1,2,3,4,5 ............ }

Step-by-step explanation:

a) As P(0) is true

we will assume that

P(2) is trueP(4) is true P(6) is true

this simply means  that ;  P(n) is true for all 'n' in the set

{ 0,2,4,6,8 ….. }

b) since P(0) and P(1) are true

we will assume that

P( 0+2 ) = P(2)  is true

also P(1) and P(2) are true

we will assume that

P(1+2) = P(3)  is true

Also from the previous answers it can be seen that P(2) + P(3) is true

we will assume

P(2+2) = P(4)  is true

This simply means that P(n) is true for all 'n' in the set

{ 0,1,2,3,4,5 ............ }

PLEASE HELP!!!! ILL GIVE BRAINLIEST!


Explain why the two figures below are not similar. Use complete sentences and provide evidence to support your explanation.

Answers

Answer: because the figure on the left is negative and more wide open while the other one is not only smaller but also positive and it’s more shut

Step-by-step explanation:

So the X-axis of the Figure on the left is going form point -3 to 0 while the other figure on the right is going form 3 to 5. And the Y- axis of the figure on the left is 2 while the right is 1 which proves that the figure on the left is bigger then the other

Your Also supposed to add all the point like first look for the Y and the X of I with J Then look for H and K then look for G and L the look for the slope of all those and then add them,then do the same with the left one and see which ones more and how much more

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