a. f(x) = x2-5x-14 b. f(x) = 9x2 -4
c. f(x) = 6x2 -x -12
factor the following
b)
$\displaystyle f(x)= 9x^2 - 4 $
$\displaystyle f(x)= (3x+2)(3x-2) $
This is known as a difference of squares when factoring. When both numbers can be square root to get an even number, it is a difference of squares, notice how the even square root is in both brackets, with opposite signs distributing to;
$\displaystyle f(x)= 9x^2 - 4 $
c.
$\displaystyle f(x)= 6x^2 - x - 12 $
$\displaystyle f(x)= (2x-3)(3x+4) $
Again, simply find the numbers that multiply to -12 and add to -x. Always remember the last sign in the equation, it is very important. If it is negative, the signs will be difference in the set of brackets. If it is positive the signs will be the same, they will both be what the first sign is.