Posted by Aaron on Saturday, May 5, 2012 at 12:07am.
Treat it like a long division. First, work out how many times 6b goes into 42b^3, which is 7b^2, and that will be the first term of your answer. Now multiply (6b+5) by 7b^2, and you'll get 42b^3 + 35b^2. Write that underneath the original expression and subtract it from it: you'll get (-12b^2 + 38b + 49).
Next, you need to work out how many times (6b+5) goes into that. To find that, ask how many times 6b goes into -12b^2, which is -2b, and that will be the next term in your answer. Multiply (6b+5) by -2b, and you'll get (-12b^2 - 10b). Subtract that from (-12b^2 + 38b + 49), and you'll get (48b + 49). But now you've got a problem, because(6b+5) doesn't divide that exactly: the closest you can get is 8, which would make your answer (7b^2 - 2b + 8). But that would only work if your final term were 40 instead of 49. Are you sure you haven't copied it down wrong?