Factoring $3x^2 - 10x + 5$ How can $3x^2 - 10x + 5$ be factored? FOIL seemingly doesn't work (15 has no factors that sum to -10).

You can always use the general formula for a quadratic equation, if we have $ax^2+bx+c$ then let $$x_1=\frac{-b+\sqrt{b^2-4ac}}{2a}$$ and $$x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}$$ then we can write $$ax^2+bx+c=a(x-x_1)(x-x_2)$$ so in particular if we have $3x^2-10x+5$ then $$x_1=\frac{10+\sqrt{40}}{6}$$ and $$x_2=\frac{10-\sqrt{40}}{6}$$ which implies that $$3x^2-10x+5=3(x-\frac{10+\sqrt{40}}{6})(x-\frac{10-\sqrt{40}}{6}).$$
