How to factorize a trinomial with fractions as terms, take in mind that I want to do it the fast way I was trying:
$$\frac{5}{12}x^2+x-\frac{8}{3}$$ I was trying with the quick algorithm but bailed to find the terms, notice I multiply the first term with the last:
$$x^2+x-\frac{10}{9}$$
$$(x+a)(x-b)$$
is there any other faster way to do it? or a quick way to find the terms?without fractions, I use prime decomposition to find the terms
quick algorithm reference:youtube.com/shorts/tXNUD8NCmcU
You could multiply through by the least common denominator, then factor the new expression, then factor out the lcd.
For example, you could multiply your example quadratic by twelve to get:
$$12\Big(\frac{5}{12}x^2 + x − \frac{8}{3}\Big) = 5x^2 + 12x - 32 = (5x - 8)(x + 4)$$
where the final factorization is using whatever techniques you know from the integer coefficient case. Once we have this, we can just put a $1/12$ at the beginning:
$$\frac{5}{12}x^2 + x − \frac{8}{3} = \frac{1}{12}(5x - 8)(x + 4)$$