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

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2 Answers

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: x1,2={-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)

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