Answer :
Answer:
Step-by-step explanation:
Main Answer:
35. By performing long division, the quotient of (24x^2 - x - 8) divided by (4x^2 + 7)** is **6 - (55x + 52)/(4x^2 + 7).
Supporting Explanation:
To perform long division, we divide the highest degree term of the numerator by the highest degree term of the denominator. In this case, we divide 24x^2 by 4x^2, which gives us 6. We then multiply the entire denominator (4x^2 + 7) by 6 and subtract it from the numerator (24x^2 - x - 8). This gives us -55x - 52.
Since the degree of -55x - 52 is less than the degree of the denominator, we bring down the next term, which is -x. We repeat the process, dividing -x by 4x^2, which gives us -0.25x. We then multiply the entire denominator by -0.25x and subtract it from the previous result (-55x - 52). This gives us -0.25x - 52.
Since the degree of -0.25x - 52 is still less than the degree of the denominator, we bring down the last term, which is -8. We repeat the process again, dividing -8 by 4x^2, which gives us -2. We then multiply the entire denominator by -2 and subtract it from the previous result (-0.25x - 52). This gives us -0.25x + 104.
At this point, the degree of -0.25x + 104 is lower than the degree of the denominator (4x^2 + 7), and we have no more terms to bring down. Therefore, our final quotient is 6 - (55x + 52)/(4x^2 + 7).
Similarly,
36. Perform long division for (3x - 2) divided by (3x - 2).
Divide 3x by 3x, which gives 1.
Multiply (3x - 2) by 1 and subtract it from (3x - 2).
Since the degrees of the remaining terms are both zero, the division is complete.
The resulting quotient is 1.
37. Perform long division for (x⁴ - 3x² + 2) divided by 3x⁴.
Divide x⁴ by 3x⁴, which gives 1/3.
Multiply 3x⁴ by 1/3 and subtract it from (x⁴ - 3x² + 2).
Continue dividing the remaining terms until no more terms can be brought down.
The resulting quotient is 1/3 - 3x²/(3x⁴).
38. Perform long division for (x² - 1) divided by (x² - 1).
Divide x² by x², which gives 1.
Multiply (x² - 1) by 1 and subtract it from (x² - 1).
Since the degrees of the remaining terms are both zero, the division is complete.
The resulting quotient is 1.
39. Perform long division for (5x³ + 13x² - x + 2) divided by (x² - 3x + 1).
Divide 5x³ by x², which gives 5x.
Multiply (x² - 3x + 1) by 5x and subtract it from (5x³ + 13x² - x + 2).
Continue dividing the remaining terms until no more terms can be brought down.
The resulting quotient is 5x - 2 + (-2x + 4)/(x² - 3x + 1).
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