Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Find reliable answers to your questions from a wide community of knowledgeable experts on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
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
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
