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Mathematics 29 Online
OpenStudy (anonymous):

factor 6x^2-31x+35

OpenStudy (anonymous):

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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

x=7/2,5/3

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