Answer:
See below.
Step-by-See below.step explanation:
If the coefficient of x^2 is 1 then you can quite easily factor it by looking at the factors of the last (constant) term.
For example;
Factor x^2 - 2x - 3.
We need 2 numbers whose product is the last term (-3) and whose sum is the coefficient of x (-2).
Now -3 times + 1 = -3 and -3 + 1 = -2, so the 2 numbers are -3 and + 1 ( remember to include the signs),
Now we simply place the -3 and + 1 after the x 's in the 2 parentheses :
= (x - 3)(x + 1) and these are the factors.
The most challenging is when we have a coefficient of x^2 greater than 1.
For example
f(x) = 4x^2 - 4x - 3.
I find the 'ac' method easier in these cases.
Lets factor the above:
The 'a' in ac refers to the coefficient of x^2 which is 4 in this case and the 'c' is -3.
Now ac , that is a times c = 4*-3 = -12.
Now we need 2 numbers whose product is -12 and whose sum = -4 ( that is the coefficient of x in f(x).
These 2 numbers are -6 and +2, so we write the function as follows, replacing the middle term - 4x by + 2x - 6x:
F(x) = 4x^2 + 2x - 6x - 3
Now we should be able to factor this by grouping , taking 2 pairs and factoring each of them.
f(x) = 2x(2x + 1) - 3(2x + 1)
(2x + 1) is common so the factors are:
f(x) = (2x - 3)(2x + 1).
Note if you had replaced the -4x by -6x + 2x ( the other way around) you wouldn't be able to get the common factor so you would just reverse them and try again.
