# Confusing Explanation in Elementary Algebra by Hall & Knight

In the chapter on Highest Common Factors (HCF's), a method is given for finding the HCF of compound expressions.

Could someone please explain the explanation given at the end of the page? The given explanation makes no sense to me.

We have $$8x^3-2x^2-53x-39$$ and $$4x^3-3x^2-24x-9$$.
To eliminate $$x^3$$ from the first equation we subtract twice the second equation from the first to obtain $$4x^2-5x-21.$$ We can now eliminate $$x^3$$ fro the second equation by subtracting $$x$$ times $$4x^2-5x-21.$$ This gives$$2x^2-3x-9.$$