15x^2-23x-21 /3x-7
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(15x^2-23x-21) / (3x-7) ?
are we graphing y = (15x^2-23x-21) / (3x-7) ?
are we solving (15x^2-23x-21) / (3x-7) = 0 ?
In any case, wolframalpha.com is your friend. It can confirm the results you get through your hard work:
http://www.wolframalpha.com/input/?i=%2815x^2-23x-21%29+%2F+%283x-7%29
To simplify the expression (15x^2 - 23x - 21)/(3x - 7), we can use the method of polynomial long division. Here are the steps to follow:
1. Set up the division, with the dividend (15x^2 - 23x - 21) as the numerator and the divisor (3x - 7) as the denominator.
2. Begin by dividing the first term of the numerator (15x^2) by the first term of the denominator (3x). The result is (15x^2)/(3x) = 5x.
3. Multiply the divisor (3x - 7) by the quotient obtained in step 2 (5x) to get 5x(3x - 7) = 15x^2 - 35x.
4. Subtract the product obtained above from the numerator. (15x^2 - 23x - 21) - (15x^2 - 35x) = -23x + 35x - 21 = 12x - 21.
5. Bring down the next term from the numerator (-21) to create the new dividend (12x - 21).
6. Divide the first term of the new dividend (12x) by the first term of the divisor (3x), giving (12x)/(3x) = 4.
7. Multiply the divisor (3x - 7) by the quotient obtained in step 6 (4) to get 4(3x - 7) = 12x - 28.
8. Subtract the product obtained above from the new dividend. (12x - 21) - (12x - 28) = -21 + 28 = 7.
9. There are no more terms to bring down from the numerator, so we are left with a remainder of 7.
10. The simplified form of the expression is the quotient obtained so far (5x + 4) with the remainder (7) over the divisor (3x - 7).
Therefore, (15x^2 - 23x - 21)/(3x - 7) simplifies to 5x + 4 + 7/(3x - 7).