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
According to the stem-and-leaf plot above, how many trees are less than 640
andreev551 [17]

Answer:

14 trees is less than 640 inches

5 0
3 years ago
manav drives from his home to the nearest metro station at an average speed of 40 kmph. from the station, he boards a train that
julia-pushkina [17]

Answer:

24 km

Step-by-step explanation:

4 0
1 year ago
1) Twice a number decreased by four is 32.<br> What is the number?
jeyben [28]

Answer:

6

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Joe is building a fort for his little brother out of boxes. He is wondering how much room there will be inside the fort.
Levart [38]
The answer is 0.5m cubed.
8 0
2 years ago
Which statement correctly compares the numbers 269,317 and 296,317?
MrRissso [65]

Your answer is c, because 69,000 is less than 96,000. I hope this helped! Could I possibly get brainliest?

5 0
3 years ago
Read 2 more answers
Other questions:
  • Select the two binomials that are factors of this trinomial.
    12·1 answer
  • If a°, 30° and 2a° are the angle of triangle find a°​
    5·1 answer
  • Under-over 7 is a very simple game played with two dice. the player simply bets on whether the sum of the two dice when rolled w
    10·1 answer
  • Janine wants to set up a play list with 8 songs on her IPod. She has 50 songs to choose from, including 15 songs by one directio
    14·1 answer
  • Please need help on this
    15·1 answer
  • Which is bigger 5/9 or 11/20
    12·1 answer
  • The table shows values for the two functions fand
    8·1 answer
  • A survey of 350 people found 150 like birds. 170 like squirrels and 30 like both animals. How many like neither?
    10·1 answer
  • Consider the right triangle below. A right triangle with a hypotenuse with length 6.5 feet, and side lengths of 2.5 feet and 6 f
    9·1 answer
  • Help please thank u!! ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!