Dividing 8x³ - 6x² + 23x + 25 by 4x + 3 will yield a quotient of 2x² - 3x + 8 and a remainder of 1.
Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.
We shall divide the expression 8x³ - 6x² + 23x + 25 by 4x + 3 as follows;
8x³ divided by 4x equals 2x²
4x + 3 multiplied by 2x² equals 8x³ + 6x²
subtract 8x³ + 6x² from 8x³ - 6x² + 23x + 25 will result to -12x² + 23x + 25
-12x² divided by 4x equals -3x
4x + 3 multiplied by -3x equals -12x² - 9x
subtract -12x² - 9x from -12x² + 23x + 25 will result to 32x + 25
32x divided by 4x equals 8
4x + 3 multiplied by 8 equals 32x + 24
subtract 32x + 24 from 32x + 25 will result to a remainder of 1.
Therefore by the long division method, 8x³ - 6x² + 23x + 25 divided by 4x + 3 gives a quotient 2x² - 3x + 8 and a remainder of 1.