divide(long division) x²+4x-12byx-2
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Answer:
x+6.
Step-by-step explanation:
To simplify the expression (x² + 4x - 12) / (x - 2), we can use polynomial long division. Here are the steps:
1. Divide the first term of the numerator (x²) by the first term of the denominator (x). The result is x.
2. Multiply the entire denominator (x - 2) by the result from step 1 (x), and write the product (x² - 2x) below the numerator.
3. Subtract the product obtained in step 2 from the numerator (x² + 4x - 12) by subtracting term by term:
(x² + 4x - 12) - (x² - 2x) = 6x - 12
4. Bring down the next term from the numerator (-12) and repeat the process.
5. Divide the first term of the new numerator (6x) by the first term of the denominator (x). The result is 6.
6. Multiply the entire denominator (x - 2) by the result from step 5 (6), and write the product (6x - 12) below the new numerator.
7. Subtract the product obtained in step 6 from the new numerator (6x - 12) by subtracting term by term:
(6x - 12) - (6x - 12) = 0
8. There is no remainder, so the division is complete.
The simplified expression is x + 6.