What is a good first step when factoring a trinomial with a negative leading coefficient?

Question

Can I please see an example of this? Also how do you factor -3x^2 +10x -3?

Answer 1

-3x^2 +10x -3

= -(3x^2 -10x +3)

= -(3x-1)(x-3) <==Answer

Ideas: Take "-" sign out first.

 

Answer 2

Any trinomial of the type ax²+bx+c can be factored as follows: a*(x-x₁)*(x-x₂), where x₁ and x₂ are the roots of quadratic equation ax²+bx+c=0;

So, in your case, -3x²+10x-3 can be factored as follows:

1) Let us solve -3x²+10x-3=0;

Quadratic formula gives us: x_1,2={-10±√[10²-4*(-3)*(-3)]}/(2*(-3))=(-10±√64)/-6;

x₁=3; x₂=1/3;

2) Let us write the factorization:

-3x²+10x-3=(-3)*(x-3)*(x-1/3) ;

Factor (-3) can be distributed into the second parentheses to obtain more compact expression:

-3x²+10x-3=(x-3)*(1-3x)