1answer.
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
ankoles [38]
3 years ago
11

The binomial x-2 is a factor of the polynomial below. f(x)=x3+x2+nx+10 What is the value of n?

Mathematics
1 answer:
Nutka1998 [239]3 years ago
3 0
<h3>Answer: n = -11</h3>

=========================================================

Explanation:

Since x-2 is a factor of f(x), this means f(2) = 0.

More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

So if we plugged x = 2 into f(x), we'd get

f(x) = x^3+x^2+nx+10

f(2) = 2^3+2^2+n(2)+10

f(2) = 8+4+2n+10

f(2) = 2n+22

Set this equal to 0 and solve for n

2n+22 = 0

2n = -22

n = -22/2

n = -11 is the answer

Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10

Plug x = 2 into that updated f(x) function to find....

f(x) = x^3+x^2-11x+10

f(2) = 2^3+2^2-11(2)+10

f(2) = 8+4-22+10

f(2) = 0

Which confirms our answer.

You might be interested in
Halp me please. This questions is killing me. I need the answer. Solve $3a + 4b = a - 8b + 24$ for $a$ in terms of $b$.
Anuta_ua [19.1K]

Answer:

a=12-6b

Step-by-step explanation:

move b and a to their respective sides, getting a = -6b+12

tada :)

3 0
3 years ago
F(x) = -2x + 9, find x if f(x) = 23
JulijaS [17]

Answer:

x = -7

Step-by-step explanation:

f(x) = -2x + 9

f(x) = 23

therefore, f(x) =

-2x + 9 = 23

     -2x = 23 - 9

     -2x = 14

       -x = 14 ÷ 2

       -x = 7

        x = -7

7 0
3 years ago
Can someone please help me and show the steps? Thank you
Maksim231197 [3]
0.348 is the answer
3 0
3 years ago
72 ounces in 6 steaks
Alona [7]

The unit rate is the total ounces divided by the total number of steaks:

72 ounces / 6 steaks = 12 ounces per steak.

3 0
3 years ago
Consider the distance formula d=16t^2 where d is the distance in feet that an object travels and t is the time in seconds that i
SIZIF [17.4K]

Answer:

The Formula D 16t 2

The formula s=16t^2 is used to approximate the distance s, in feet, that an object falls freely from the rest in t seconds. The height of a building is. The formula s=16t^2 is used to approximate the distance s, in feet, that an object falls freely from the rest in t seconds.

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • A cup of coffee has approximately 310 mg of caffeine. Each hour, the caffeine in your system decreases by about 35%. How much ca
    8·1 answer
  • A survey of 1010 college seniors working towards an undergraduate degree was conducted. each student was asked, "are you plannin
    11·1 answer
  • 8p+8=10+7p what is the solution set
    12·2 answers
  • Find the equation the line with the given information below:
    5·1 answer
  • Find the area of a circle with diameter 10 cm . Use the value 3.14 for π , and do not round your answer. Be sure to include the
    5·1 answer
  • What number is228% of 14.5
    10·1 answer
  • What is the factored form of the function f(x)=x^3+8x^2+5x−50?
    13·1 answer
  • Help please <br> 3 |X-4| +1 = 19
    7·1 answer
  • Use a​ table, an​ equation, and a graph to represent the relationship below.
    6·2 answers
  • If the perimeter of an equilateral triangle is 30cm, find its area. ​
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!