Question

factor 6x^2-31x+35

Answer 1

When you find it hard to factorize a polynomial, simply find its roots using the quadratic formula.
\[ x = \frac {-b\pm\sqrt{b^2-4ac}} {2a} \]
If the roots are α and β, then the equation will be of the form
\[ a(x-\alpha)(x-\beta) \]
where a is a constant.

If you do that, you will find that the roots are 5/3 and 7/2.

So the original equation should be a multiple of
\[ (x-\frac53)(x-\frac72) = x^2 - \frac{31}6x+\frac{35}6 \]
It is quite obvious at this point that the constant a will be 6. (compare the coefficients of x².

Does this help?

Answer 2

=(2x-7)(3x-5)

Answer 3

x=7/2,5/3