(x − 2) is a factor of x4 + 2x3 − 7x2 − 8x + 12. The other factors are ___, ___, and ___.
Answers
The all other 3 factors of the equation x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3).
What are the roots of an equation?
Roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.
For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.
Given the equation,
x⁴ + 2x³ − 7x² − 8x + 12
If (x - 2) is a factor of the equation then it should be divisible by it.
So,
(x⁴ + 2x³ − 7x² − 8x + 12) / (x - 2) = (x³ + 4x² + x - 6)
Now divide by (x - 1) of (x³ + 4x² + x - 6)
(x³ + 4x² + x - 6) / (x - 1) = x² + 5x + 6
So,
⇒ (x - 2)(x - 1)(x² + 5x + 6)
⇒ (x - 2)(x - 1)( x² + 2x + 3x + 6)
⇒ (x - 2)(x - 1)[ x(x + 2) + 3(x + 2) ]
⇒ (x - 2)(x - 1)(x + 2)(x + 3)
Hence "The all other 3 factors of the equation x⁴ + 2x³ − 7x² − 8x + 12 will b e(x + 2),(x - 1) and (x + 3)".
To learn more about the roots of an equation,
#SPJ2
Answer:
Step-by-step explanation:
The given equation is:
Now, (x-2) is a factor of the given equation, therefore
Therefore, the other factors are (x-1), (x+2) and (x+3).
Related Questions
The possible outcomes for tossing a coin four times are shown below.1. T-T-T-T 5. T-H-T-T 9. H-T-T-T 13. H-H-T-T 2. T-T-T-H 6. T-H-T-H 10. H-T-T-H 14. H-H-T-H 3. T-T-H-T 7. T-H-H-T 11. H-T-H-T 15. H-H-H-T 4. T-T-H-H 8. T-H-H-H 12. H-T-H-H 16. H-H-H-H Tails = T Heads = H If a coin is tossed four times, what is the probability of getting exactly zero heads?
What is the growth factor associated with the following growth rate: 30% decrease Your answer should be typed as a decimal.
What is slope of the line that passes through (1,4) and (1,-3)
Given the following information, determine if one of the brands is a better buy.Brand A: 14 ounces for $44.66 Brand B: 20 ounces for $63.80 a. Both brands cost the same per ounce. b. Brand A is the better buy. c. Brand B is the better buy. d. There is not enough information provided to determine the better buy.
Answers
Answer:
x = 2
Step-by-step explanation:
x SR20 = 7 SR5 - SR45
x = (7 SR5 - SR45) / SR20
x = 2
Answers
what is 1/3 and negative 9/20 as decimals??
Answers
in the denominator of a fraction. 'x' to negative 3rd power is the same as 1/x³ .
1/x³ = 27/64
Take the reciprocal of each side:
x³ = 64/27
x= ∛64/27 = ∛64 / ∛27.
64 is the perfect cube of 4.
27 is the perfect cube of 3.
x = 4/3 .
Answers
Answer:
Step-by-step explanation:
prime
composite
neither
Answers
Answer:
28 is even.
It is divisible by 2,4,28,7,14
It is composite ( has more than 2 factors)
Step-by-step explanation:
Took the test :)
Answers
Final answer:
To find out how long it takes for the temperature of the roast to drop to 110 F, we can use the Newton's Law of Cooling equation. By setting up and solving a differential equation, we find that it takes approximately 34 minutes for the temperature of the roast to drop to 110 F.
Explanation:
To find out how long it takes for the temperature of the roast to drop to 110 F, we can use the Newton's Law of Cooling equation. This equation states that the rate of change of temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings.
In this case, we can write the equation as: dT/dt = -k(T - Troom),
where dT/dt represents the rate of change of temperature with respect to time, T is the temperature of the roast, Troom is the temperature of the room, and k is a constant.
We know that when the roast was taken out of the oven, its temperature was 165 F, and after 15 minutes, its temperature dropped to 135 F. Using these values, we can set up the initial value problem:
dT/dt = -k(T - 70), T(0) = 165
Solving this differential equation, we find the value of k to be 1/15. Using this value, we can find the time it takes for the temperature to drop to 110 F:
dT/dt = -1/15(T - 70)
Integration of the equation gives: ln|T - 70| = -t/15 + C
Using the initial condition T(0) = 165, we can find the value of the constant C as: ln|165 - 70| = 0 + C
Therefore, C = ln(95).
Substituting back into the equation, we get:
ln|T - 70| = -t/15 + ln(95)
T - 70 = e^(-t/15 + ln(95))
T = 70 + 25e^(-t/15)
Now, we can substitute T = 110 and solve for t:
110 = 70 + 25e^(-t/15)
25e^(-t/15) = 40
e^(-t/15) = 40/25
-t/15 = ln(40/25)
t = -15ln(40/25)
Simplifying, we find that it takes approximately 34 minutes for the temperature of the roast to drop to 110 F.
Learn more about Newton's Law of Cooling here:
#SPJ2