Quadratics vs trinomial factoring

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Hi all,

I’ve got this really dumb question that I can’t wrap my head around.

So I get that the factored form of a quadratic equation from ax^(2) + bx + c is: a (x – r₁) (x – r₂).

But when factoring a trinomial with a leading coefficient, you would factor it like: (cx – r₁)(dx – r₂). For example: 6x^(2) – 5x + 1= (2x-1)(3x-1). Wouldn’t this also be the factored form of a quadratic, if not, then why?

Thanks

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1 Answer

Anonymous 0 Comments

It really depends on your end-goal. If you’re in a class and the professor asks for one way or the other, then your end goal is making the professor happy.

When we are looking for the zeros in an equation:

6(x – 1/2)(x – 1/3)

makes it clearer that x = 1/2 and x = 1/3 are the zeros, however, if the equation is going to be the denominator of a rational expression the fractions are generally considered a bad thing.