find the remainder when the polynomial f(x)=12xcube -13x^-5x+7 is divided (3x+2)
To find the remainder when the polynomial f(x) = 12x^3 - 13x^2 - 5x + 7 is divided by (3x + 2), we can use synthetic division.
1. First, set up the synthetic division table by writing down the coefficients of the polynomial f(x) in descending order:
| 12 -13 -5 7
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2. Next, write down the root of the divisor (3x + 2) as its opposite value, changing the sign:
| 12 -13 -5 7
----------------------
-2
3. Bring down the first coefficient (12) and multiply it by the root (-2), then write the result below the second coefficient (-13):
| 12 -13 -5 7
24
4. Add the second coefficient (-13) with the result of the previous calculation (24), and write the sum below the third coefficient (-5):
| 12 -13 -5 7
24
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11
5. Repeat steps 3 and 4 with the new sum (11):
| 12 -13 -5 7
24 -22
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11 -27
6. Finally, add the third coefficient (-5) with the result of the previous calculation (-27), and write the sum below the last coefficient (7):
| 12 -13 -5 7
24 -22
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11 -27
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-20
The remainder is the last number on the bottom row of the synthetic division table, which is -20. Therefore, the remainder when f(x) is divided by (3x + 2) is -20.
did you mean:
(12x^3 - 13x^2 - 5x + 7) ÷ (3x+2) ?
verify
if so, simply find f(-2/3) , using the remainder theorem