Question

Which of the following is the complete factorization of 10x - 3 - 3x 2?

Answer 1

-3x^2+10x-3  

This is of the form ax^2+bx+c.  We need to find two values, j and k, such that:

jk=ac=9 and j+k=b=10, so j and k must be 1 and 9.

Now replace bx with jx and kx in the original equation...

-3x^2+x+9x-3  now factor 1st and 2nd pair of terms

-x(3x-1)+3(3x-1)

(-x+3)(3x-1) or equivalently...

-(x-3)(3x-1) or as they put it:

-(3x-1)(x-3)