You would use long division for polynomials, very similar to the long division for numbers.
Each digit in the long division will be replaced by the coefficient of the powers of b.
Dividing by 5b+3,
gives the first "digit" of the quotient as 5b²
Subtract 25b³+15b² from the original expression gives an expression one degree lower:
(25b^3+5b^2+34b+29) - 25b³+15b²
Continuing this way will give the complete quotient.
See for reference:
go to webmathcom, click algebra and under simplifying expressions click anything else and enter your promblem and hit try to simplify it and it will explain everything
Your webpage did a lousy job of the problem,
your answer is not correct, it is simply the original numerator.
(How can the exponent of the first term stay the same ?????)