Answer:
Explanation:
To simplify the expression (12x^3 - 7x^2 + 24x + 26)/(4x + 3), we can use long division. Here are the steps:
1. Divide the first term of the numerator (12x^3) by the first term of the denominator (4x). The result is 3x^2.
2. Multiply the denominator (4x + 3) by the result obtained in step 1 (3x^2). The product is 12x^3 + 9x^2.
3. Subtract the product obtained in step 2 from the numerator (12x^3 - 7x^2 + 24x + 26) and write the result below.
12x^3 - 7x^2 + 24x + 26
- (12x^3 + 9x^2)
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-16x^2 + 24x + 26
4. Bring down the next term from the numerator, which is 24x.
-16x^2 + 24x + 26
5. Divide the first term of the new expression (-16x^2) by the first term of the denominator (4x). The result is -4x.
6. Multiply the denominator (4x + 3) by the result obtained in step 5 (-4x). The product is -16x^2 - 12x.
7. Subtract the product obtained in step 6 from the new expression (-16x^2 + 24x + 26) and write the result below.
-16x^2 + 24x + 26
- (-16x^2 - 12x)
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36x + 26
8. Bring down the last term from the numerator, which is 26.
36x + 26
9. Divide the first term of the new expression (36x) by the first term of the denominator (4x). The result is 9.
10. Multiply the denominator (4x + 3) by the result obtained in step 9 (9). The product is 36x + 27.
11. Subtract the product obtained in step 10 from the new expression (36x + 26) and write the result below.
36x + 26
- (36x + 27)
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-1
12. The remainder is -1.
Therefore, the simplified expression is 3x^2 - 4x + 9 - 1/(4x + 3).