answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fomenos
2 years ago
12

What is the completely factored form of f(x)=x3+5x2+4x−6?

Mathematics
1 answer:
Gre4nikov [31]2 years ago
3 0
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
You might be interested in
How to write 75 1/3 % as a fraction in simplest form
Snowcat [4.5K]
75 1/3 = 75.33

75.33% = 75.33/100 
              = 7533/10000
 
 not sure if it can be simplified more than this        
3 0
2 years ago
Read 2 more answers
A researcher is estimating the mean income of residents in a large city. The income variable is usually skewed to the right. She
Gnom [1K]

Answer: We are 95% confident that the mean income for all residents of this city is between $26700 and $35400.

Step-by-step explanation:

We know that a 95% confidence interval given an interval of values that we can be 95% sure , that it contains the true mean of the population, not 95% of data lies in it.

Given : A researcher is estimating the mean income of residents in a large city. The income variable is usually skewed to the right. She collects a random sample of 25 people.

The resulting 95% confidence interval is ($26700, $35400).

Then, valid conclusion will be :  We are 95% confident that the mean income for all residents of this city is between $26700 and $35400.

5 0
2 years ago
Which explanation provides the best real-world scenario of the graph?
Naddika [18.5K]
The last one is the only one that makes sense according to the standard position function.  -16t^2 is the pull of gravity on an object in free fall, and the height is 120 feet above the ground.  Hopefully that's what you need since there's no graph we can refer to
5 0
2 years ago
Read 2 more answers
There are 8 candidates for student government: Hal, Mary, Ann, Frank, Beth, John, Emily, and Tom. The three candidates that rece
sveticcg [70]

Answer:

56

Step-by-step explanation:

Given that there are 8 candidates for student government: Hal, Mary, Ann, Frank, Beth, John, Emily, and Tom.

The three candidates that receive the highest number of votes become candidates for a runoff election.

i.e. 3 persons out of 8 to be selected for becoming candidates for a runoff election.

Since order does not matter we use combinations here

3 persons out of 8 can be done in 8C3 ways

= 56

no of 3-candidate combinations  possible are 56

3 0
2 years ago
Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not ad
soldier1979 [14.2K]

pH = f(x) = -log₁₀x

1. Graphs

I used Excel to calculate the pH values and draw the graphs (see the Figure).

f(x) and f(x) +1 are plotted against the left-hand axis, while f(x+ 1) is plotted against the expanded right-hand axis.

The points at which pH = 0 and pH = 1 are indicated by the large red dots.

2. x = 0.5

When x = 0.5, pH ≈0.30. The point is indicated by the red diamond.

3. Transformations

(a) ƒ(x) = -log(x) + 1

This function has no y-intercept, because log(0) is undefined.

(b) ƒ(x +1) = -log(x + 1)

f(0) = -log(0 + 1) = -log(1) = 0

This function has a y-intercept at (0,0).

hope this helps please mark me brainliest!

3 0
2 years ago
Other questions:
  • A jump rope held stationary by two children, one at each end, hangs in a shape that can be modeled by the equation h=0.01x^2 - x
    6·2 answers
  • A jar contains 5 blue marbles, 7 yellow marbles, and 8 green marbles. What is the probability of randomly choosing a blue marble
    13·1 answer
  • Erica is given the diagram below and asked to prove that ab df. What would be the missing step of the proof? I only need the ans
    7·2 answers
  • Firewood is stacked in a pile. The bottom row has 20 logs, and the top row was 14 logs. Each row has one more log than the row a
    5·2 answers
  • How many different triangles can you make if you are given the measurement for two angles in the length of a side that is NOT sh
    7·2 answers
  • In Drew's town the average price for a tutor is $15 per hour, and the standard deviation is $5.25 per hour. In Drew's town, what
    11·1 answer
  • Calvin's school is 2.3 miles directly south of his house. After school, he takes a bus 1.8 miles directly west to the sports com
    9·1 answer
  • Orthographic projection and isometric projection are two ways to show three-dimensional objects in a two-dimensional space, such
    12·1 answer
  • Solve the equation the square root of the quantity x plus 4 minus 3 equals 1 for the variable. Show each step of your solution p
    13·2 answers
  • Help marking Brainly!!!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!