What is the quotient of ##b^3 + 4b^2 – 3b + 126## by b+7?

##b^2-3b+18##

Use long division, as used for integers, to find the quotient.

The divisor is ##b+7##. Look at the first term of the dividend, i.e. ##b^3##.

What should be multiplied to ##b## (of the divisor) to get the first term of the dividend, i.e. ##b^3##?

##bxx b^2=b^3## Therefore, ##b^2## becomes the first term of the quotient.

Now, ##b^2 xx (b+7)=b^3 + 7b^2## Write it below the corresponding terms of the dividend and subtract.

We are now left with ##-3b^2-3b+126##.

Repeat.