Question 91465
Factor:
{{{2z^2-z-6}}} 
First, find the factors of the leading coefficient (that's the 2).
There is only one possibility and that's 1*2
So you can start by writing (2x + m)(x + n)
Now m*n must be equal to -6 (the consatnt term in the quadratic equation) so the possibilities are:
m*n = -6 So you know that m and n will have opposite signs
-1*6 = -6 (m = -1 and n = 6)
1*(-6) = -6 (m = 1 and n = -6)
-2*3 = -6 (m = -2 and n = 3)
2*(-3) = -6 (m = 2 and n = -3)
You also know that 2(n)+m = -1 (This is the coefficient of the z-term).
So we try:
(2z+3)(z-2) Using FOIL to multiply, we get:
{{{2z^2-4z+3z-6}}} Combining like-terms, we get:
{{{2z^2-z-6}}}
So the factors are:
(2z+3)(z-2)