4а^3-8а^2-3а-6/а^2-4

Question 1

Задача Задача №121091

А

Аноним

15 декабря 2023 16:57 · публичный вопрос

А

Аноним 15 декабря 2023 16:57

4а^3-8а^2-3а-6/а^2-4

Answer

To simplify the expression (4a^3 - 8a^2 - 3a - 6) divided by (a^2 - 4), we can use polynomial long division. Here are the steps:

Step 1: Set up the expression in long division format: ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6

Step 2: Divide the first term of the numerator (4a^3) by the first term of the denominator (a^2). The result is 4a.

          4a
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6

Step 3: Multiply the divisor (a^2 - 4) by the quotient (4a). The result is 4a^3 - 16a.

          4a
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a)

Step 4: Subtract the above result from the numerator.

          4a
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6

Step 5: Now, we need to divide the first term of the new numerator (8a^2) by the first term of the denominator (a^2). The result is 8.

          4a + 8
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6

Step 6: Multiply the divisor (a^2 - 4) by the new quotient (8). The result is 8a^2 - 32.

          4a + 8
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32)

Step 7: Subtract the above result from the numerator.

          4a + 8
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26

Step 8: Now, we need to divide the last term of the new numerator (13a) by the first term of the denominator (a^2). The result is 13.

          4a + 8 + 13/(a-2)
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26

Step 9: Multiply the divisor (a^2 - 4) by the new quotient (13). The result is 13a - 52.

          4a + 8 + 13/(a-2)
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 - (13a - 52)

Step 10: Subtract the above result from the numerator.

          4a + 8 + 13/(a-2)
      ___________________

a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 - (13a - 52) ___________________ 26

So, the simplified expression is 4a + 8 + 13/(a-2).

Question 2

4а^3-8а^2-3а-6/а^2-4

Answer

To simplify the expression (4a^3 - 8a^2 - 3a - 6) divided by (a^2 - 4), we can use polynomial long division. Here are the steps: Step 1: Set up the expression in long division format: ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 Step 2: Divide the first term of the numerator (4a^3) by the first term of the denominator (a^2). The result is 4a. 4a ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 Step 3: Multiply the divisor (a^2 - 4) by the quotient (4a). The result is 4a^3 - 16a. 4a ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) Step 4: Subtract the above result from the numerator. 4a ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 Step 5: Now, we need to divide the first term of the new numerator (8a^2) by the first term of the denominator (a^2). The result is 8. 4a + 8 ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 Step 6: Multiply the divisor (a^2 - 4) by the new quotient (8). The result is 8a^2 - 32. 4a + 8 ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) Step 7: Subtract the above result from the numerator. 4a + 8 ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 Step 8: Now, we need to divide the last term of the new numerator (13a) by the first term of the denominator (a^2). The result is 13. 4a + 8 + 13/(a-2) ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 Step 9: Multiply the divisor (a^2 - 4) by the new quotient (13). The result is 13a - 52. 4a + 8 + 13/(a-2) ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 - (13a - 52) Step 10: Subtract the above result from the numerator. 4a + 8 + 13/(a-2) ___________________ a^2 - 4 | 4a^3 - 8a^2 - 3a - 6 - (4a^3 - 16a) ___________________ 8a^2 + 13a - 6 - (8a^2 - 32) ___________________ 13a - 26 - (13a - 52) ___________________ 26 So, the simplified expression is 4a + 8 + 13/(a-2).