+68 9 = (r-2)(2r+sqrt5)(2r-sqrt5)
10 = (7k+6)(3k^2+8)
11 = (6x+7)(sqrt7x+sqrt6)(sqrt7x-sqrt6)
12 = (p+6)(p+sqrt3)((p-sqrt3)
+118667 Given a rough inspection I think they are all the same sort of factorization.
So if I do the first one and you understand then you are capable of doing the other three yourself.
9)
\(4r^3-8r^2-5r+10\\ =4r^3-8r^2\qquad\qquad -5r+10\\ \text{now factorize the pairs}\\ =4r^2(r-2)\qquad\qquad -5(r-2)\\\)
now you can think of (r-2) as just one thing.
So you have \(4r^2\) lots of (r-2) and then you take away \(5\) lots of (r-2)
That will give you \((4r^2-5)\) lots of (r-2)
which is
\((4r^2-5)(r-2)\)
you could take this one step further by treating \(4r^2-5\) as the difference of 2 squares
\(4r^2 = (2r)^2 \) and \(5=(\sqrt5)^2 \) so
\((4r^2-5) = (2r-\sqrt5)(2r+\sqrt5)\)
\((4r^2-5)(r-2)=(2r-\sqrt5)(2r+\sqrt5)(r-2)\)
