Question

What is the result of the division: (2x³ - 5x) / (4x - 3)?

a) 1/2 x² + 3/8 x + 9/32
b) 1/2 x² - 3/8 x + 9/32
c) 2x² + 3/4 x + 9/32
d) 2x² - 3/4 x + 9/32

Answer 1

To divide (2x³ - 5x) by (4x - 3), use long division. The quotient is 1/2x² - (3/8)x + (9/32). Hence, option B is correct.

Step-by-step explanation:

To divide the polynomial (2x³ - 5x) by (4x - 3), we use long division. Here are the steps:

1. Divide the first term of the numerator (2x³) by the first term of the denominator (4x). This gives you 1/2x².
2. Multiply the result from step 1 (1/2x²) by the denominator (4x - 3). This gives you 1/2x² * (4x - 3) = 2x³ - (3/2)x².
3. Subtract the result from step 2 (2x³ - (3/2)x²) from the numerator (2x³ - 5x). This gives you (2x³ - 5x) - (2x³ - (3/2)x²) = - (3/2)x² - 5x.
4. Repeat steps 1-3 with the new numerator (- (3/2)x² - 5x). This will give you the next term of the quotient.
5. Continue this process until you no longer have any terms left in the numerator.

After completing the long division, the quotient is 1/2x² - (3/8)x + (9/32). Therefore, the correct answer is b) 1/2 x² - 3/8 x + 9/32.