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
CaHeK987 [17]
2 years ago
9

Use the long division method to find the result when x^3+9x² +21x +9 is divided by x+3

Mathematics
1 answer:
Serhud [2]2 years ago
5 0

Answer:

x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

Step-by-step explanation:

Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: Set up the polynomial long division problem with a division bracket, putting the numerator inside and the denominator on the left:

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

To eliminate the leading term of the numerator, x^3, multiply x + 3 by x^2 to get x^3 + 3 x^2. Write x^2 on top of the division bracket and subtract x^3 + 3 x^2 from x^3 + 9 x^2 + 21 x + 9 to get 6 x^2 + 21 x + 9:

| | | x^2 | | | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

To eliminate the leading term of the remainder of the previous step, 6 x^2, multiply x + 3 by 6 x to get 6 x^2 + 18 x. Write 6 x on top of the division bracket and subtract 6 x^2 + 18 x from 6 x^2 + 21 x + 9 to get 3 x + 9:

| | | x^2 | + | 6 x | |

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

To eliminate the leading term of the remainder of the previous step, 3 x, multiply x + 3 by 3 to get 3 x + 9. Write 3 on top of the division bracket and subtract 3 x + 9 from 3 x + 9 to get 0:

| | | x^2 | + | 6 x | + | 3

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9

| -(x^3 | + | 3 x^2) | | | |

| | | 6 x^2 | + | 21 x | + | 9

| | | -(6 x^2 | + | 18 x) | |

| | | | | 3 x | + | 9

| | | | | -(3 x | + | 9)

| | | | | | | 0

The quotient of (x^3 + 9 x^2 + 21 x + 9)/(x + 3) is the sum of the terms on top of the division bracket. Since the final subtraction step resulted in zero, x + 3 exactly divides x^3 + 9 x^2 + 21 x + 9 and there is no remainder.

| | | x^2 | + | 6 x | + | 3 | (quotient)

x + 3 | x^3 | + | 9 x^2 | + | 21 x | + | 9 |

| -(x^3 | + | 3 x^2) | | | | |

| | | 6 x^2 | + | 21 x | + | 9 |

| | | -(6 x^2 | + | 18 x) | | |

| | | | | 3 x | + | 9 |

| | | | | -(3 x | + | 9) |

| | | | | | | 0 | (remainder) invisible comma

(x^3 + 9 x^2 + 21 x + 9)/(x + 3) = (x^2 + 6 x + 3) + 0

Write the result in quotient and remainder form:

Answer: x^3 + 9 x^2 + 21 x + 9 = (x^2 + 6 x + 3)×(x + 3) + 0

You might be interested in
Graph and solve the system <br><br> Y=-3x+3<br> Y=2x-7
guajiro [1.7K]
An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.

They are called "linear" because if we draw all the solutions of such an equation, they form a line. 

This also means that it is enough to:
 
1. find to solutions 
2. plot them on the coordinate axis
3.join those 2 points

and all the solutions of the equation y=ax+b will be on that line.


Thus, to draw line y=-3x+3

let x=0, then y=3, so one solution is (0, 3)

let y=0, then x=1 so a second solution is (1, 0)

(remark we can pick x or y to be any value, then solve for the other)


to draw the second line y=2x-7

let x=0, then y=-7
let x=3, then y=-1


plot these points and join them as shown in the picture.


The solution of the system is the point where the lines intersect, which is
 (2, -3)


8 0
3 years ago
Read 2 more answers
HELPPPP ASAP 1.Go to the website for the U.S. Bureau of Labor Statistics: www.bls.gov. Under the Subject Areas tab, look under P
lakkis [162]

Answer:

do you still need help for the answer?

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Whats your favorite color? (free points)<br><br> :)
aniked [119]

Answer:

My favourite color is The Red and White;)

What's yours?

don't forget to like and mark me

6 0
2 years ago
Read 2 more answers
Which of the following is equal to the fraction below?
Crazy boy [7]

Answer:the answer should be c


Step-by-step explanation:So, the 11 is an exponent. That means that the problem can be written as 11 x 7/4 so it should be c.


6 0
3 years ago
Read 2 more answers
Question 10 (1 point)
Diano4ka-milaya [45]

Answer:

borh are correct in the same order that you wrote them. fist you eliminate 1 from the orinal side to the other so the next step is also right you subtrac 8 mines 1 so equal to 7 ...

6 0
3 years ago
Other questions:
  • What is the probability that the sun will rise tommorow?​
    11·2 answers
  • Kendra gets a paycheck of $300 after 5 days of work.At this rate,how much does she get paid for working 24 days?
    7·2 answers
  • What polynomial identity should be used to prove that 16^2=(10+6)^2? (A. Difference of Cubes; B. Difference of Squares; C. Squar
    12·2 answers
  • Depending on the day of the week, a border guard searches every nth person coming across the border. Each Tuesday every 7th pers
    14·1 answer
  • What is pie time the square root of 9
    8·1 answer
  • PLS HELP QUICKLY!
    15·2 answers
  • PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*.. <br> IM GIVING 40 POINTS !! DONT SKIP :((.
    6·1 answer
  • You and your friend are playing a game by tosing two coins land on different sides your friend wins the table shows the possible
    12·1 answer
  • To find the height of a giant ice cream cone outside of an ice cream parlor, Jayda places a mirror on the ground 320 inches from
    11·1 answer
  • Translate the point (5,2)—&gt; 3 units to the left
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!