229k views
0 votes
3. (x³ + 3x²-x + 2)÷(x - 1)?? How do you divide using long division?!?

User CubeJockey
by
8.6k points

1 Answer

4 votes

Answer:

(x³ + 3x² - x + 2) ÷ (x - 1) equals x² + 4x - 3 with a remainder of -1.

Explanation:

! :To divide the polynomial (x³ + 3x² - x + 2) by (x - 1) using long division, follow these steps:

Step 1: Write the dividend (x³ + 3x² - x + 2) and divisor (x - 1) in long division format:

___________________

(x - 1) | x³ + 3x² - x + 2

Step 2: Divide the first term of the dividend (x³) by the first term of the divisor (x):

___________________

(x - 1) | x³ + 3x² - x + 2

Step 3: Multiply the divisor (x - 1) by the quotient obtained in step 2 (x²). Write the result below the dividend, aligned with the corresponding term:

___________________

(x - 1) | x³ + 3x² - x + 2

x² + ...

x³ - x²

Step 4: Subtract the result obtained in step 3 (x³ - x²) from the dividend (x³ + 3x² - x + 2):

___________________

(x - 1) | x³ + 3x² - x + 2

x² + ...

_______________

4x² - x

Step 5: Bring down the next term from the dividend, which is -x, and continue the process:

___________________

(x - 1) | x³ + 3x² - x + 2

x² + ... - 4x

4x² - x

_______________

-3x + 2

Step 6: Bring down the last term from the dividend, which is +2, and continue the process:

___________________

(x - 1) | x³ + 3x² - x + 2

x² + ... - 4x - 3

4x² - x

_______________

-3x + 2

-3x + 3

Step 7: Divide the last term of the dividend (-3x + 2) by the first term of the divisor (x):

___________________

(x - 1) | x³ + 3x² - x + 2

x² + ... - 4x - 3

4x² - x

_______________

-3x + 2

-3x + 3

_______

-1

Step 8: Write the remainder (-1) as the last term of the result.

The final result is:

Quotient: x² + 4x - 3

Remainder: -1

User Avinashbot
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories