Sometimes things are best without accompanying text. Use the following solution progression as a supplement to the above explanation.
l) (2x + 3)(x - 9)
= 2x2 -18x +3x -27
= 2x2 - 15x - 27
ll) -4(x +2)²
= -4x2 - 16x - 16
lol@ "factorize," feel free to just say "I need to factor these"
l) -x² -2x + 35
In general its not good to have a negative leading coefficient. Factor out a negative sign:
-(x2 +2x -35)
You need a pair of numbers which multiply to negative 35 and add to 2.
7 and -5 work:
Solutions are -7 and 5 (where either binomial is equal to zero)
ll) 3x² - 75
As was the case in the precious problem, where the leading coefficient was -1, we had problems. Just like in the last problem, let's factor out something from the expression so that the x^2 term has a coefficient of 1:
3(x2 - 25)
Here you have an expression of the form (x2 - a2), where a is some number (in this case 5, since 5^2 =25). This is one of those handy dandy circumstances that you need to memorize:
(x2 - a2) = (x + a)(x - a)
So your factored expression is:
Solutions are 5 or -5