Step 1: Divide the leading term of the dividend by the leading term of the divisor.
2x^3 / 2x = x^2
Step 2: Multiply the divisor by the quotient obtained in Step 1.
(x^2)(2x + 5) = 2x^3 + 5x^2
Step 3: Subtract the result obtained in Step 2 from the dividend.
(2x^3 + x^2 + 0x + 25) - (2x^3 + 5x^2) = -4x^2 + 0x + 25
Step 4: Bring down the next term from the dividend.
-4x^2 + 0x + 25
Step 5: Divide the leading term of the new dividend by the leading term of the divisor.
-4x^2 / 2x = -2x
Step 6: Multiply the divisor by the quotient obtained in Step 5.
(-2x)(2x + 5) = -4x^2 - 10x
Step 7: Subtract the result obtained in Step 6 from the new dividend.
(-4x^2 + 0x + 25) - (-4x^2 - 10x) = 10x + 25
Step 8: Bring down the next term from the dividend.
10x + 25
Step 9: Divide the leading term of the new dividend by the leading term of the divisor.
10x / 2x = 5
Step 10: Multiply the divisor by the quotient obtained in Step 9.
(5)(2x + 5) = 10x + 25
Step 11: Subtract the result obtained in Step 10 from the new dividend.
(10x + 25) - (10x + 25) = 0
Step 12: Since the new dividend is zero, we stop the division.
Therefore, the quotient of (2x^3 + x^2 + 25) divided by (2x + 5) is x^2 - 2x + 5.