I distributed 3x^2+x-10=f(x) to find the zeroes. My book's answer was (3x-5)(x+2). When I distributed this to make sure I got the original function, I got 3x^2-x-10. Is this still an acceptable way to factor it even though the x is negative instead of positive as it should be? I got the answers the book got through this method (5/3 and -2) But I don't see how this can be correct with the x being negative.

Question

I distributed 3x^2+x-10=f(x) to find the zeroes.  My book's answer was (3x-5)(x+2).  When I distributed this to make sure I got the original function, I got 3x^2-x-10.  Is this still an acceptable way to factor it even though the x is negative instead of positive as it should be? I got the answers the book got through this method (5/3 and -2) But I don't see how this can be correct with the x being negative.

MathMate · Answer

Use FOIL (3x-5)(x+2) =3x*x + 3x*2 -5*x -5(2) =3x² + 6x -5x -10 =3x² + x -10 as in the original expresion, and the answer is correct.