<PRE><B>Question 292844</B>
Divide.

(10x^2 + 13x - 3) ÷ (5x - 1)


{{{(10x^2 + 13x - 3)/(5x - 1)}}}


We first need to get the factors of the trinomial in the numerator. Therefore, {{{10x^2 + 13x - 3}}} becomes {{{10x^2 + 15x - 2x - 3}}}, and then becomes: 5x(2x + 3) - 1(2x + 3), or (5x - 1)(2x + 3).


We will then have: {{{(5x - 1)(2x + 3)/(5x - 1)}}}, or {{{cross((5x - 1))(2x + 3)/cross((5x - 1))}}}


Canceling (5x - 1) in the numerator and denominator gives us a final answer of: {{{highlight_green(2x + 3)}}}. </PRE>