Question

Can someone explain to me how f(x)=3x^2-20x-32 factors into (3x+4)(x-8)? I just don't get the process of how you come up with that.

Answer 1

first you should know that if it can be broken to factors it should be like,

\((ax+b)(cx+d)\)

then if we take the coefficients of x^2, it is 3. therefore \(ac\) has to be equal to 3 since there is only one possibility of getting 3 from multiplying 2 integers (ie 1x3), we can assign a=3 and c = 1

\((3x+b)(x+d)\)

now take constants from above the constant is bd which should be equal to -32
\(bd = -32\)

and consider coefficients of x similarly,
\(b+3d=-20\)

either you can solve the above two equation or just do the whole process in mind

Answer 2

Nice! I've always had trouble understanding that. Just wrote this down in my notes and will be using it. Thank for your help!